{"id":557,"date":"2020-08-21T19:41:08","date_gmt":"2020-08-21T23:41:08","guid":{"rendered":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/solve-geometry-applications-volume-and-surface-area\/"},"modified":"2021-03-24T10:53:33","modified_gmt":"2021-03-24T14:53:33","slug":"solve-geometry-applications-volume-and-surface-area","status":"publish","type":"chapter","link":"https:\/\/opentextbc.ca\/introalgebra\/chapter\/solve-geometry-applications-volume-and-surface-area\/","title":{"raw":"3.3 Solve Geometry Applications: Volume and Surface Area","rendered":"3.3 Solve Geometry Applications: Volume and Surface Area"},"content":{"raw":"[latexpage]\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nBy the end of this section, you will be able to:\n<ul>\n \t<li>Find volume and surface area of rectangular solids<\/li>\n \t<li>Find volume and surface area of spheres<\/li>\n \t<li>Find volume and surface area of cylinders<\/li>\n \t<li>Find volume of cone<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p id=\"fs-id1931140\">In this section, we will find the volume and surface area of some three-dimensional figures. Since we will be solving applications, we will once again show our Problem-Solving Strategy for Geometry Applications.<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Problem Solving Strategy for Geometry Applications<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<ol class=\"stepwise\" type=\"1\">\n \t<li><strong data-effect=\"bold\">Read<\/strong> the problem and make sure you understand all the words and ideas. Draw the figure and label it with the given information.<\/li>\n \t<li><strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/li>\n \t<li><strong data-effect=\"bold\">Name<\/strong> what you are looking for. Choose a variable to represent that quantity.<\/li>\n \t<li><strong data-effect=\"bold\">Translate<\/strong> into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.<\/li>\n \t<li><strong data-effect=\"bold\">Solve<\/strong> the equation using good algebra techniques.<\/li>\n \t<li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem and make sure it makes sense.<\/li>\n \t<li><strong data-effect=\"bold\">Answer<\/strong> the question with a complete sentence.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Find Volume and Surface Area of Rectangular Solids<\/h1>\nA cheer leading coach is having the squad paint wooden crates with the school colors to stand on at the games. (See <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_06_001\">Figure.1<\/a>). The amount of paint needed to cover the outside of each box is the surface area, a square measure of the total area of all the sides. The amount of space inside the crate is the volume, a cubic measure.\n<div id=\"CNX_BMath_Figure_09_06_001\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">This wooden crate is in the shape of a rectangular solid.<\/div>\n\n[caption id=\"\" align=\"aligncenter\" width=\"374\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_09_06_001.jpg\" alt=\"This is an image of a wooden crate.\" width=\"374\" height=\"227\" data-media-type=\"image\/jpeg\"> Figure.1[\/caption]\n<p id=\"fs-id1475627\">Each crate is in the shape of a rectangular solid. Its dimensions are the length, width, and height. The rectangular solid shown in <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_06_002\">Figure.2<\/a> has length \\(4\\) units, width \\(2\\) units, and height \\(3\\) units. Can you tell how many cubic units there are altogether? Let\u2019s look layer by layer.<\/p>\nBreaking a rectangular solid into layers makes it easier to visualize the number of cubic units it contains. This \\(4\\) by \\(2\\) by \\(3\\) rectangular solid has \\(24\\) cubic units.\n<div id=\"CNX_BMath_Figure_09_06_002\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"507\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_002.jpg\" alt=\"A rectangular solid is shown. Each layer is composed of 8 cubes, measuring 2 by 4. The top layer is pink. The middle layer is orange. The bottom layer is green. Beside this is an image of the top layer that says \u201cThe top layer has 8 cubic units.\u201d The orange layer is shown and says \u201cThe middle layer has 8 cubic units.\u201d The green layer is shown and says, \u201cThe bottom layer has 8 cubic units.\u201d\" width=\"507\" height=\"133\" data-media-type=\"image\/jpeg\"> Figure.2[\/caption]\n<p id=\"fs-id1171487599067\">Altogether there are \\(24\\) cubic units. Notice that \\(24\\) is the \\(\\text{length}\\phantom{\\rule{1.0em}{0ex}}\\times\\phantom{\\rule{1.0em}{0ex}}\\text{width}\\phantom{\\rule{1.0em}{0ex}}\\times\\phantom{\\rule{1.0em}{0ex}}\\text{height}\\text{.}\\)<\/p>\n<span id=\"fs-id1171498001442\" data-type=\"media\" data-alt=\"The top line says V equals L times W times H. Beneath the V is 24, beneath the equal sign is another equal sign, beneath the L is a 4, beneath the W is a 2, beneath the H is a 3.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_002_img.jpg\" alt=\"The top line says V equals L times W times H. Beneath the V is 24, beneath the equal sign is another equal sign, beneath the L is a 4, beneath the W is a 2, beneath the H is a 3.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1171505120230\"><strong>The volume, \\(V\\), of any rectangular solid is the product of the length, width, and height.<\/strong><\/p>\n<strong>\\(V=LWH\\)<\/strong>\n<p id=\"fs-id1171488252104\">We could also write the formula for volume of a rectangular solid in terms of the area of the base. The area of the base, \\(B\\), is equal to \\(\\text{length}\\times\\text{width}\\text{.}\\)<\/p>\n\n<div id=\"fs-id1171104062309\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(\\text{B}=\\text{L}\\cdot\\text{W}\\)<\/div>\n<p id=\"fs-id1793392\">We can substitute \\(\\text{B}\\) for \\(\\text{L}\\cdot\\text{W}\\) in the volume formula to get another form of the volume formula.<\/p>\n<span id=\"fs-id1171506203641\" data-type=\"media\" data-alt=\"The top line says V equals red L times red W times H. Below this is V equals red parentheses L times W times H. Below this is V equals red capital B times h.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_003_img.jpg\" alt=\"The top line says V equals red L times red W times H. Below this is V equals red parentheses L times W times H. Below this is V equals red capital B times h.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1933170\">We now have another version of the volume formula for rectangular solids. Let\u2019s see how this works with the \\(4\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}2\\phantom{\\rule{0.2em}{0ex}}\\times\\phantom{\\rule{0.2em}{0ex}}3\\) rectangular solid we started with. See <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_06_004\">Figure.3<\/a>.<\/p>\n\n<div id=\"CNX_BMath_Figure_09_06_004\" class=\"bc-figure figure\">\n\n<img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_004_img.jpg\" alt=\"An image of a rectangular solid is shown. It is made up of cubes. It is labeled as 2 by 4 by 3. Beside the solid is V equals Bh. Below this is V equals Base times height. Below Base is parentheses 4 times 2. The next line says V equals parentheses 4 times 2 times 3. Below that is V equals 8 times 3, then V equals 24 cubic units.\" width=\"302\" height=\"118\" data-media-type=\"image\/jpeg\">\n<h3>Figure.3<\/h3>\n<\/div>\n<p id=\"fs-id1171505368262\">To find the <em data-effect=\"italics\">surface area<\/em> of a rectangular solid, think about finding the area of each of its faces. How many faces does the rectangular solid above have? You can see three of them.<\/p>\n\\(\\begin{array}{ccccccc}{A}_{\\text{front}}=L\\times W\\hfill &amp; &amp; &amp; {A}_{\\text{side}}=L\\times W\\hfill &amp; &amp; &amp; {A}_{\\text{top}}=L\\times W\\hfill \\\\ {A}_{\\text{front}}=4\\cdot3\\hfill &amp; &amp; &amp; {A}_{\\text{side}}=2\\cdot3\\hfill &amp; &amp; &amp; {A}_{\\text{top}}=4\\cdot2\\hfill \\\\ {A}_{\\text{front}}=12\\hfill &amp; &amp; &amp; {A}_{\\text{side}}=6\\hfill &amp; &amp; &amp; {A}_{\\text{top}}=8\\hfill \\end{array}\\)\n\nNotice for each of the three faces you see, there is an identical opposite face that does not show.\n\n\\(\\begin{array}{l}S=\\left(\\text{front}+\\text{back}\\right)\\text{+}\\left(\\text{left side}+\\text{right side}\\right)+\\left(\\text{top}+\\text{bottom}\\right)\\\\ S=\\left(2\\cdot\\text{front}\\right)+\\left(\\text{2}\\cdot\\text{left side}\\right)+\\left(\\text{2}\\cdot\\text{top}\\right)\\\\ S=2\\cdot12+2\\cdot6+2\\cdot8\\\\ S=24+12+16\\\\ S=52\\phantom{\\rule{0.2em}{0ex}}\\text{sq. units}\\end{array}\\)\n<p id=\"fs-id1418671\">The surface area \\(S\\) of the rectangular solid shown in <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_06_004\">(Figure.3)<\/a> is \\(52\\) square units.<\/p>\nIn general, to find the surface area of a rectangular solid, remember that each face is a rectangle, so its area is the product of its length and its width (see <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_06_005\">Figure.4<\/a>). Find the area of each face that you see and then multiply each area by two to account for the face on the opposite side.\n\n\\(S=2LH+2LW+2WH\\)\n\nFor each face of the rectangular solid facing you, there is another face on the opposite side. There are \\(6\\) faces in all.\n<div id=\"CNX_BMath_Figure_09_06_005\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"156\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_005.jpg\" alt=\"A rectangular solid is shown. The sides are labeled L, W, and H. One face is labeled LW and another is labeled WH.\" width=\"156\" height=\"173\" data-media-type=\"image\/jpeg\"> Figure.4[\/caption]\n\n<div id=\"fs-id1658379\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Volume and Surface Area of a Rectangular Solid<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n\nFor a rectangular solid with length \\(L\\), width \\(W\\), and height \\(H:\\)\n\n<span id=\"fs-id1686239\" data-type=\"media\" data-alt=\"A rectangular solid is shown. The sides are labeled L, W, and H. Beside it is Volume: V equals LWH equals BH. Below that is Surface Area: S equals 2LH plus 2LW plus 2WH.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_006_img.jpg\" alt=\"A rectangular solid is shown. The sides are labeled L, W, and H. Beside it is Volume: V equals LWH equals BH. Below that is Surface Area: S equals 2LH plus 2LW plus 2WH.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1178399\">For a rectangular solid with length \\(14\\) cm, height \\(17\\) cm, and width \\(9\\) cm, find the a) volume and b) surface area.<\/p>\n\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1594850\">Step 1 is the same for both a) and b), so we will show it just once.<\/p>\n\n<table id=\"eip-id1168468779989\" class=\"unnumbered unstyled\" summary=\"The text reads, \u201cStep 1. Read the problem. Draw the figure and label it with the given information.\u201d Beside this is an image of a rectangular solid. It is labeled 14 by 9 by 17.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and\nlabel it with the given information.<\/td>\n<td><span id=\"eip-id1168468780014\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_038_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468454551\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the rectangular solid<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let \\(V\\)= volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute.<\/td>\n<td>\\(V=LWH\\)\n\\(V=\\mathrm{14}\\cdot 9\\cdot 17\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td>\\(V=2,142\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check<\/strong>\nWe leave it to you to check your calculations.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The surface area is \\(\\text{1,034}\\) square centimetres.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168469477419\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the surface area of the solid<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let \\(S\\)= surface area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute.<\/td>\n<td>\\(S=2LH+2LW+2WH\\)\n\\(S=2\\left(14\\cdot 17\\right)+2\\left(14\\cdot 9\\right)+2\\left(9\\cdot 17\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve the equation.<\/strong><\/td>\n<td>\\(S=1,034\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Double-check with a calculator.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The surface area is 1,034 square centimetres.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1658281\" data-type=\"problem\">\n<p id=\"fs-id1406524\">Find the a) volume and b) surface area of rectangular solid with the: length \\(8\\) feet, width \\(9\\) feet, and height \\(11\\) feet.<\/p>\n\n<\/div>\n<div id=\"fs-id1171506137807\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168466313772\" class=\"circled\" type=\"a\">\n \t<li>792 cu. ft<\/li>\n \t<li>518 sq. ft<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1171505624033\" data-type=\"exercise\">\n<div id=\"fs-id1658281\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1563070\" data-type=\"problem\">\n<p id=\"fs-id1171505480381\">Find the a) volume and b) surface area of rectangular solid with the: length \\(15\\) feet, width \\(12\\) feet, and height \\(8\\) feet.<\/p>\n\n<\/div>\n<div id=\"fs-id1932667\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168466312554\" class=\"circled\" type=\"a\">\n \t<li>1,440 cu. ft<\/li>\n \t<li>792 sq. ft<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1602274\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1171516922529\" data-type=\"exercise\">\n<div id=\"fs-id1563070\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171498355737\" data-type=\"problem\">\n\nA rectangular crate has a length of \\(30\\) inches, width of \\(25\\) inches, and height of \\(20\\) inches. Find its a) volume and b) surface area.\n\n<\/div>\n<div id=\"fs-id1592712\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1528864\">Step 1 is the same for both a) and b), so we will show it just once.<\/p>\n\n<table id=\"eip-id1168467275051\" class=\"unnumbered unstyled\" summary=\"The text reads, \u201cStep 1. Read the problem. Draw the figure and label it with the given information.\u201d Beside this is an image of a rectangular solid. It is labeled 30 by 25 by 20.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and\nlabel it with the given information.<\/td>\n<td><span id=\"eip-id1168468779962\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_039_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467238054\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the crate<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let \\(V\\)= volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute.<\/td>\n<td>\\(V=LWH\\)\n\\(V=30\\cdot 25\\cdot 20\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td>\\(V=15,000\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Double check your math.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume is 15,000 cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467505864\" class=\"unnumbered unstyled\" style=\"height: 130px;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 290.406px;\">b)<\/td>\n<td style=\"height: 14px; width: 469.406px;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 290.406px;\">Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td style=\"height: 14px; width: 469.406px;\">the surface area of the crate<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 290.406px;\">Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td style=\"height: 14px; width: 469.406px;\">let \\(S\\)= surface area<\/td>\n<\/tr>\n<tr style=\"height: 46px;\">\n<td style=\"height: 46px; width: 290.406px;\">Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute.<\/td>\n<td style=\"height: 46px; width: 469.406px;\">\\(S=2LH+2LW+2WH\\)\n\\(S=2\\left(30\\cdot 20\\right)+2\\left(30\\cdot 25\\right)+2\\left(25\\cdot 20\\right)\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 290.406px;\">Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td style=\"height: 14px; width: 469.406px;\">\\(S=3,700\\)<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 290.406px;\">Step 6. <strong data-effect=\"bold\">Check:<\/strong> Check it yourself!<\/td>\n<td style=\"height: 14px; width: 469.406px;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 290.406px;\">Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td style=\"height: 14px; width: 469.406px;\">The surface area is 3,700 square inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1394700\" data-type=\"problem\">\n\nA rectangular box has length \\(9\\) feet, width \\(4\\) feet, and height \\(6\\) feet. Find its a) volume and b) surface area.\n\n<\/div>\n<div id=\"fs-id1171505547241\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168468373746\" class=\"circled\" type=\"a\">\n \t<li>216 cu. ft<\/li>\n \t<li>228 sq. ft<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1762464\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2064891\" data-type=\"exercise\">\n<div id=\"fs-id1171505547241\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1608864\" data-type=\"problem\">\n<p id=\"fs-id1171506673948\">A rectangular suitcase has length \\(22\\) inches, width \\(14\\) inches, and height \\(9\\) inches. Find its a) volume and b) surface area.<\/p>\n\n<\/div>\n<div id=\"fs-id1171506207477\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168469802778\" class=\"circled\" type=\"a\">\n \t<li>2,772 cu. in.<\/li>\n \t<li>1,264 sq. in.<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Volume and Surface Area of a Cube<\/h1>\n<p id=\"fs-id1171505481979\">A cube is a rectangular solid whose length, width, and height are equal. See Volume and Surface Area of a Cube, below. Substituting, <em data-effect=\"italics\">s<\/em> for the length, width and height into the formulas for volume and surface area of a rectangular solid, we get:<\/p>\n\\(\\begin{array}{ccccc}V=LWH\\hfill &amp; &amp; &amp; &amp; S=2LH+2LW+2WH\\hfill \\\\ V=\\text{s}\\cdot\\text{s}\\cdot\\text{s}\\hfill &amp; &amp; &amp; &amp; S=2\\text{s}\\cdot\\text{s}+2\\text{s}\\cdot\\text{s}+2\\text{s}\\cdot\\text{s}\\hfill \\\\ V={\\text{s}}^{3}\\hfill &amp; &amp; &amp; &amp; S=2{s}^{2}+2{s}^{2}+2{s}^{2}\\hfill \\\\ &amp; &amp; &amp; &amp; S=6{s}^{2}\\hfill \\end{array}\\)\n<p id=\"fs-id1767806\">So for a cube, the formulas for volume and surface area are \\(V={s}^{3}\\) and \\(S=6{s}^{2}\\).<\/p>\n\n<div id=\"fs-id1560075\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Volume and Surface Area of a Cube<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1516282\">For any cube with sides of length \\(s\\),<\/p>\n<span id=\"fs-id1171496258265\" data-type=\"media\" data-alt=\"An image of a cube is shown. Each side is labeled s. Beside this is Volume: V equals s cubed. Below that is Surface Area: S equals 6 times s squared.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_010_img.jpg\" alt=\"An image of a cube is shown. Each side is labeled s. Beside this is Volume: V equals s cubed. Below that is Surface Area: S equals 6 times s squared.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171496189268\" data-type=\"problem\">\n<p id=\"fs-id1171505620889\">A cube is \\(2.5\\) inches on each side. Find its a) volume and b) surface area.<\/p>\n\n<\/div>\n<div id=\"fs-id1585408\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1784097\">Step 1 is the same for both a) and b), so we will show it just once.<\/p>\n\n<table id=\"eip-id1168466154480\" class=\"unnumbered unstyled\" summary=\"The text reads, \u201cStep 1. Read the problem. Draw the figure and label it with the given information.\u201d Beside this is an image of a cube. It is labeled 2.5 by 2.5 by 2.5.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and\nlabel it with the given information.<\/td>\n<td><span id=\"eip-id1168469766852\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_040_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168465993815\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the cube<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.<\/td>\n<td>\\(V={s}^{3}\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong> Substitute and solve.<\/td>\n<td>\\(V={\\left(2.5\\right)}^{3}\\)\n\\(V=15.625\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Check your work.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume is 15.625 cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168466275896\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the surface area of the cube<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">S<\/em> = surface area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.<\/td>\n<td>\\(S=6{s}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong> Substitute and solve.<\/td>\n<td>\\(S=6\\cdot {\\left(2.5\\right)}^{2}\\)\n\\(S=37.5\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> The check is left to you.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The surface area is 37.5 square inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1489297\" data-type=\"problem\">\n<p id=\"fs-id1529247\">For a cube with side 4.5 metres, find the a) volume and b) surface area of the cube.<\/p>\n\n<\/div>\n<div id=\"fs-id1933234\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168466248223\" class=\"circled\" type=\"a\">\n \t<li>91.125 cu. m<\/li>\n \t<li>121.5 sq. m<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1452349\" data-type=\"exercise\">\n<div id=\"fs-id1489297\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171487571769\" data-type=\"problem\">\n\nFor a cube with side 7.3 yards, find the a) volume and b) surface area of the cube.\n\n<\/div>\n<div id=\"fs-id1529140\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168467222372\" class=\"circled\" type=\"a\">\n \t<li>389.017 cu. yd.<\/li>\n \t<li>319.74 sq. yd.<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1590812\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1418268\" data-type=\"exercise\">\n<div id=\"fs-id1171487571769\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171506138160\" data-type=\"problem\">\n<p id=\"fs-id1171505934498\">A notepad cube measures \\(2\\) inches on each side. Find its a) volume and b) surface area.<\/p>\n\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168467296950\" class=\"unnumbered unstyled\" summary=\"The text reads, \u201cStep 1. Read the problem. Draw the figure and label it with the given information.\u201d Beside this is an image of a cube. It is labeled 2 by 2 by 2.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and\nlabel it with the given information.<\/td>\n<td><span id=\"eip-id1168467496838\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_041_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467188434\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the cube<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.<\/td>\n<td>\\(V={s}^{3}\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td>\\(V={2}^{3}\\)\n\\(V=8\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Check that you did the calculations\ncorrectly.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume is 8 cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468478236\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the surface area of the cube<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">S<\/em> = surface area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.<\/td>\n<td>\\(S=6{s}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td>\\(S=6\\cdot {2}^{2}\\)\n\\(S=24\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> The check is left to you.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The surface area is 24 square inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1927378\" data-type=\"problem\">\n<p id=\"fs-id1871924\">A packing box is a cube measuring \\(4\\) feet on each side. Find its a) volume and b) surface area.<\/p>\n\n<\/div>\n<div id=\"fs-id1171511527503\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168466072253\" class=\"circled\" type=\"a\">\n \t<li>64 cu. ft<\/li>\n \t<li>96 sq. ft<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1038661\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2058174\" data-type=\"exercise\">\n<div id=\"fs-id1171511527503\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1927378\" data-type=\"problem\">\n<p id=\"fs-id1871924\">A packing box is a cube measuring \\(4\\) feet on each side. Find its a) volume and b) surface area.<\/p>\n\n<\/div>\n<div id=\"fs-id1171511527503\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168466072253\" class=\"circled\" type=\"a\">\n \t<li>64 cu. ft<\/li>\n \t<li>96 sq. ft<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Find the Volume and Surface Area of Spheres<\/h1>\n<p id=\"fs-id1954343\">A sphere is the shape of a basketball, like a three-dimensional circle. Just like a circle, the size of a sphere is determined by its radius, which is the distance from the centre of the sphere to any point on its surface. The formulas for the volume and surface area of a sphere are given below.<\/p>\n<p id=\"eip-745\">Showing where these formulas come from, like we did for a rectangular solid, is beyond the scope of this course. We will approximate \\(\\pi \\) with \\(3.14\\).<\/p>\n\n<div id=\"fs-id1171512117057\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Volume and Surface Area of a Sphere<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1171512117850\">For a sphere with radius \\(r\\text{:}\\)<\/p>\n<span id=\"fs-id1171505277582\" data-type=\"media\" data-alt=\"An image of a sphere is shown. The radius is labeled r. Beside this is Volume: V equals four-thirds times pi times r cubed. Below that is Surface Area: S equals 4 times pi times r squared.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_015.jpg\" alt=\"An image of a sphere is shown. The radius is labeled r. Beside this is Volume: V equals four-thirds times pi times r cubed. Below that is Surface Area: S equals 4 times pi times r squared.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171498454044\" data-type=\"problem\">\n<p id=\"fs-id1171498401975\">A sphere has a radius \\(6\\) inches. Find its a) volume and b) surface area.<\/p>\n\n<\/div>\n<div id=\"fs-id1650050\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1171512511594\">Step 1 is the same for both a) and b), so we will show it just once.<\/p>\n\n<table id=\"eip-id1168468504255\" class=\"unnumbered unstyled\" summary=\"The text reads, \u201cStep 1. Read the problem. Draw the figure and label it with the given information.\u201d Beside this is an image of a sphere. The radius is labeled 6.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label\nit with the given information.<\/td>\n<td><span id=\"eip-id1168468504279\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_042_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168466046693\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the sphere<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.<\/td>\n<td>\\(V=\\frac{4}{3}\\pi {r}^{3}\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td>\\(V\\approx \\frac{4}{3}\\left(3.14\\right){6}^{3}\\)\n\\(V\\approx 904.32\\phantom{\\rule{0.2em}{0ex}}\\text{cubic inches}\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Double-check your math on a calculator.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume is approximately 904.32 cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467263246\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the surface area of the cube<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">S<\/em> = surface area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.<\/td>\n<td>\\(S=4\\pi {r}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td>\\(S\\approx 4\\left(3.14\\right){6}^{2}\\)\n\\(S\\approx 452.16\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Double-check your math on a calculator<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The surface area is approximately 452.16 square inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1913002\" data-type=\"problem\">\n<p id=\"fs-id1171488074403\">Find the a) volume and b) surface area of a sphere with radius 3 centimetres.<\/p>\n\n<\/div>\n<div data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168466006411\" class=\"circled\" type=\"a\">\n \t<li>113.04 cu. cm<\/li>\n \t<li>113.04 sq. cm<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171506644186\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2091579\" data-type=\"exercise\">\n<div data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171505891413\" data-type=\"problem\">\n<p id=\"fs-id1574560\">Find the a) volume and b) surface area of each sphere with a radius of \\(1\\) foot<\/p>\n\n<\/div>\n<div id=\"fs-id748315\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168467234126\" class=\"circled\" type=\"a\">\n \t<li>4.19 cu. ft<\/li>\n \t<li>12.56 sq. ft<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171498000511\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id748315\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id945308\" data-type=\"problem\">\n<p id=\"fs-id1566505\">A globe of Earth is in the shape of a sphere with radius \\(14\\) centimetres. Find its a) volume and b) surface area. Round the answer to the nearest hundredth.<\/p>\n\n<\/div>\n<div id=\"fs-id1171488252639\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168467368787\" class=\"unnumbered unstyled\" summary=\"Step 1. Read the problem.\u201d Beside this is an image of a globe. The radius is labeled 14.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw a figure with the\ngiven information and label it.<\/td>\n<td><span id=\"eip-id1168467309173\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_043_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168464926516\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the sphere<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute. (Use 3.14 for \\(\\pi \\))<\/td>\n<td>\\(V=\\frac{4}{3}\\pi {r}^{3}\\)\n\\(V\\approx \\frac{4}{3}\\left(3.14\\right){14}^{3}\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td>\\(V\\approx 11,488.21\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> We leave it to you to check your calculations.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume is approximately 11,488.21 cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468466725\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the surface area of the sphere<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">S<\/em> = surface area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute. (Use 3.14 for \\(\\pi \\))<\/td>\n<td>\\(S=4\\pi {r}^{2}\\)\n\\(S\\approx 4\\left(3.14\\right){14}^{2}\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td>\\(S\\approx 2461.76\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> We leave it to you to check your calculations.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The surface area is approximately 2461.76 square inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1561201\" data-type=\"problem\">\n<p id=\"fs-id1398847\">A beach ball is in the shape of a sphere with radius of \\(9\\) inches. Find its a) volume and b) surface area.<\/p>\n\n<\/div>\n<div id=\"fs-id1531978\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168468772882\" class=\"circled\" type=\"a\">\n \t<li>3052.08 cu. in.<\/li>\n \t<li>1017.36 sq. in.<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1418575\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1398911\" data-type=\"exercise\">\n<div id=\"fs-id1531978\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1552724\" data-type=\"problem\">\n<p id=\"fs-id1171505276108\">A Roman statue depicts Atlas holding a globe with radius of \\(1.5\\) feet. Find the a) volume and b) surface area of the globe.<\/p>\n\n<\/div>\n<div id=\"fs-id1171511528462\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168467200300\" class=\"circled\" type=\"a\">\n \t<li>14.13 cu. ft<\/li>\n \t<li>28.26 sq. ft<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Find the Volume and Surface Area of a Cylinder<\/h1>\n<p id=\"fs-id1804291\">If you have ever seen a can of soda, you know what a cylinder looks like. A cylinder is a solid figure with two parallel circles of the same size at the top and bottom. The top and bottom of a cylinder are called the bases. The height \\(h\\) of a cylinder is the distance between the two bases. For all the cylinders we will work with here, the sides and the height, \\(h\\) , will be perpendicular to the bases.<\/p>\nA cylinder has two circular bases of equal size. The height is the distance between the bases.\n<div id=\"CNX_BMath_Figure_09_06_020\" class=\"bc-figure figure\">\n\n<span id=\"fs-id1777988\" data-type=\"media\" data-alt=\"An image of a cylinder is shown. There is a red arrow pointing to the radius of the top labeling it r, radius. There is a red arrow pointing to the height of the cylinder labeling it h, height.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_020_img.jpg\" alt=\"An image of a cylinder is shown. There is a red arrow pointing to the radius of the top labeling it r, radius. There is a red arrow pointing to the height of the cylinder labeling it h, height.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<p id=\"fs-id1772153\">Rectangular solids and cylinders are somewhat similar because they both have two bases and a height. The formula for the volume of a rectangular solid, \\(V=Bh\\) , can also be used to find the volume of a cylinder.<\/p>\n<p id=\"fs-id1748732\">For the rectangular solid, the area of the base, \\(B\\) , is the area of the rectangular base, length \u00d7 width. For a cylinder, the area of the base, \\(B\\), is the area of its circular base, \\(\\pi {r}^{2}\\). <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_06_021\">(Figure.5)<\/a> compares how the formula \\(V=Bh\\) is used for rectangular solids and cylinders.<\/p>\nSeeing how a cylinder is similar to a rectangular solid may make it easier to understand the formula for the volume of a cylinder.\n<div id=\"CNX_BMath_Figure_09_06_021\" class=\"bc-figure figure\">\n\n[caption id=\"\" align=\"aligncenter\" width=\"246\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_021.jpg\" alt=\"In (a), a rectangular solid is shown. The sides are labeled L, W, and H. Below this is V equals capital Bh, then V equals Base times h, then V equals parentheses lw times h, then V equals lwh. In (b), a cylinder is shown. The radius of the top is labeled r, the height is labeled h. Below this is V equals capital Bh, then V equals Base times h, then V equals parentheses pi r squared times h, then V equals pi times r squared times h.\" width=\"246\" height=\"286\" data-media-type=\"image\/jpeg\"> Figure.5[\/caption]\n<p id=\"fs-id1171505927833\">To understand the formula for the <span class=\"no-emphasis\" data-type=\"term\">surface area<\/span> of a cylinder, think of a can of vegetables. It has three surfaces: the top, the bottom, and the piece that forms the sides of the can. If you carefully cut the label off the side of the can and unroll it, you will see that it is a rectangle. See <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_06_022\">(Figure.6)<\/a>.<\/p>\n\n<div id=\"CNX_BMath_Figure_09_06_022\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">By cutting and unrolling the label of a can of vegetables, we can see that the surface of a cylinder is a rectangle. The length of the rectangle is the circumference of the cylinder\u2019s base, and the width is the height of the cylinder.<\/div>\n\n[caption id=\"\" align=\"aligncenter\" width=\"431\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_022.jpg\" alt=\"A cylindrical can of green beans is shown. The height is labeled h. Beside this are pictures of circles for the top and bottom of the can and a rectangle for the other portion of the can. Above the circles is C equals 2 times pi times r. The top of the rectangle says l equals 2 times pi times r. The left side of the rectangle is labeled h, the right side is labeled w.\" width=\"431\" height=\"153\" data-media-type=\"image\/jpeg\"> Figure.6[\/caption]\n<p id=\"fs-id1876089\">The distance around the edge of the can is the circumference of the cylinder\u2019s base it is also the length \\(L\\) of the rectangular label. The height of the cylinder is the width \\(W\\) of the rectangular label. So the area of the label can be represented as<\/p>\n<span id=\"fs-id1570430\" data-type=\"media\" data-alt=\"The top line says A equals l times red w. Below the l is 2 times pi times r. Below the w is a red h.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_023_img.jpg\" alt=\"The top line says A equals l times red w. Below the l is 2 times pi times r. Below the w is a red h.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1475242\">To find the total surface area of the cylinder, we add the areas of the two circles to the area of the rectangle.<\/p>\n<span id=\"fs-id1551755\" data-type=\"media\" data-alt=\"A rectangle is shown with circles coming off the top and bottom.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_044_img.jpg\" alt=\"A rectangle is shown with circles coming off the top and bottom.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1171498421446\">The surface area of a cylinder with radius \\(r\\) and height \\(h\\), is<\/p>\n\n<div id=\"fs-id1171102984009\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\">\\(S=2\\pi {r}^{2}+2\\pi rh\\)<\/div>\n<div data-type=\"equation\" data-label=\"\">\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Volume and Surface Area of a Cylinder<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1650370\">For a cylinder with radius \\(r\\) and height \\(h:\\)<\/p>\n<span id=\"fs-id1869917\" data-type=\"media\" data-alt=\"A cylinder is shown. The height is labeled h and the radius of the top is labeled r. Beside it is Volume: V equals pi times r squared times h or V equals capital B times h. Below this is Surface Area: S equals 2 times pi times r squared plus 2 times pi times r times h.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_024.jpg\" alt=\"A cylinder is shown. The height is labeled h and the radius of the top is labeled r. Beside it is Volume: V equals pi times r squared times h or V equals capital B times h. Below this is Surface Area: S equals 2 times pi times r squared plus 2 times pi times r times h.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1768322\" data-type=\"note\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1474985\" data-type=\"problem\">\n<p id=\"fs-id1553388\">A cylinder has height \\(5\\) centimetres and radius \\(3\\) centimetres. Find the a) volume and b) surface area.<\/p>\n\n<\/div>\n<div id=\"fs-id1171488254612\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"fs-id1168466110662\" class=\"unnumbered unstyled\" summary=\"The text reads, \u201cStep 1. Read the problem.\u201d Beside this is an image of a cylinder. The radius is labeled 3, the height is labeled 5.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label\nit with the given information.<\/td>\n<td><span id=\"eip-id1168468466750\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_046_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168469800646\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the cylinder<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute. (Use 3.14 for \\(\\pi \\))<\/td>\n<td>\\(V=\\pi {r}^{2}h\\)\n\\(V\\approx \\left(3.14\\right){3}^{2}\\cdot 5\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td>\\(V\\approx 141.3\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> We leave it to you to check your calculations.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume is approximately 141.3 cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468464551\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the surface area of the cylinder<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">S<\/em> = surface area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute. (Use 3.14 for \\(\\pi \\))<\/td>\n<td>\\(S=2\\pi {r}^{2}+2\\pi rh\\)\n\\(S\\approx 2\\left(3.14\\right){3}^{2}+2\\left(3.14\\right)\\left(3\\right)5\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td>\\(S\\approx 150.72\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> We leave it to you to check your calculations.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The surface area is approximately 150.72 square inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1562839\" data-type=\"problem\">\n<p id=\"fs-id1587965\">Find the a) volume and b) surface area of the cylinder with radius 4 cm and height 7cm.<\/p>\n\n<\/div>\n<div id=\"fs-id1581886\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168468741344\" class=\"circled\" type=\"a\">\n \t<li>351.68 cu. cm<\/li>\n \t<li>276.32 sq. cm<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1594311\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1334808\" data-type=\"exercise\">\n<div id=\"fs-id1581886\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1704558\" data-type=\"problem\">\n<p id=\"fs-id1762587\">Find the a) volume and b) surface area of the cylinder with given radius 2 ft and height 8 ft.<\/p>\n\n<\/div>\n<div id=\"fs-id1330308\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168466030869\" class=\"circled\" type=\"a\">\n \t<li>100.48 cu. ft<\/li>\n \t<li>125.6 sq. ft<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171487511722\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1590474\" data-type=\"exercise\">\n<div id=\"fs-id1330308\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2143886\" data-type=\"problem\">\n<p id=\"fs-id1171506152146\">Find the a) volume and b) surface area of a can of soda. The radius of the base is \\(4\\) centimetres and the height is \\(13\\) centimetres. Assume the can is shaped exactly like a cylinder.<\/p>\n\n<\/div>\n<div id=\"fs-id2103175\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168468414539\" class=\"unnumbered unstyled\" summary=\"The text reads, \u201cStep 1. Read the problem.\u201d Beside this is an image of a cylinder. The radius is labeled 4, the height is labeled 13.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and\nlabel it with the given information.<\/td>\n<td><span id=\"eip-id1168468414563\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_047_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468670924\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the cylinder<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute. (Use 3.14 for \\(\\pi \\))<\/td>\n<td>\\(V=\\pi {r}^{2}h\\)\n\\(V\\approx \\left(3.14\\right){4}^{2}\\cdot 13\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td>\\(V\\approx 653.12\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> We leave it to you to check.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume is approximately 653.12 cubic centimetres.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467199006\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the surface area of the cylinder<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">S<\/em> = surface area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute. (Use 3.14 for \\(\\pi \\))<\/td>\n<td>\\(S=2\\pi {r}^{2}+2\\pi rh\\)\n\\(S\\approx 2\\left(3.14\\right){4}^{2}+2\\left(3.14\\right)\\left(4\\right)13\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td>\\(S\\approx 427.04\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> We leave it to you to check your calculations.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The surface area is approximately 427.04 square centimetres.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171505228788\" data-type=\"problem\">\n<p id=\"fs-id1171505228790\">Find the a) volume and b) surface area of a can of paint with radius 8 centimetres and height 19 centimetres. Assume the can is shaped exactly like a cylinder.<\/p>\n\n<\/div>\n<div id=\"fs-id1792934\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168466094517\" class=\"circled\" type=\"a\">\n \t<li>3,818.24 cu. cm<\/li>\n \t<li>1,356.48 sq. cm<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1426872\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1171505275146\" data-type=\"exercise\">\n<div id=\"fs-id1792934\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1555240\" data-type=\"problem\">\n<p id=\"fs-id1612789\">Find the a) volume and b) surface area of a cylindrical drum with radius 2.7 feet and height 4 feet. Assume the drum is shaped exactly like a cylinder.<\/p>\n\n<\/div>\n<div id=\"fs-id1594954\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<ol id=\"eip-id1168467310156\" class=\"circled\" type=\"a\">\n \t<li>91.5624 cu. ft<\/li>\n \t<li>113.6052 sq. ft<\/li>\n<\/ol>\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Find the Volume of Cones<\/h1>\n<p id=\"fs-id1171505792760\">The first image that many of us have when we hear the word \u2018cone\u2019 is an ice cream cone. There are many other applications of cones (but most are not as tasty as ice cream cones). In this section, we will see how to find the volume of a cone.<\/p>\n<p id=\"fs-id1673945\">In geometry, a cone is a solid figure with one circular base and a vertex. The height of a cone is the distance between its base and the vertex.The cones that we will look at in this section will always have the height perpendicular to the base. See <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_06_029\">(Figure.6)<\/a>.<\/p>\n\n<div id=\"CNX_BMath_Figure_09_06_029\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">The height of a cone is the distance between its base and the vertex.<\/div>\n\n[caption id=\"\" align=\"aligncenter\" width=\"136\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_029.jpg\" alt=\"An image of a cone is shown. The top is labeled vertex. The height is labeled h. The radius of the base is labeled r.\" width=\"136\" height=\"132\" data-media-type=\"image\/jpeg\"> Figure.6[\/caption]\n<p id=\"fs-id1171505778220\">Earlier in this section, we saw that the volume of a cylinder is \\(V=\\pi{r}^{2}h\\). We can think of a cone as part of a cylinder. <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_06_030\">Figure.7 <\/a>shows a cone placed inside a cylinder with the same height and same base. If we compare the volume of the cone and the cylinder, we can see that the volume of the cone is less than that of the cylinder.<\/p>\n\n<div id=\"CNX_BMath_Figure_09_06_030\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">The volume of a cone is less than the volume of a cylinder with the same base and height.<\/div>\n\n[caption id=\"\" align=\"aligncenter\" width=\"104\"]<img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_030.jpg\" alt=\"An image of a cone is shown. There is a cylinder drawn around it.\" width=\"104\" height=\"138\" data-media-type=\"image\/jpeg\"> Figure.7[\/caption]\n<p id=\"fs-id1550720\">In fact, the volume of a cone is exactly one-third of the volume of a cylinder with the same base and height. The volume of a cone is<\/p>\n<span id=\"fs-id993657\" data-type=\"media\" data-alt=\"The formula V equals one-third times capital B times h is shown.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_031_img.jpg\" alt=\"The formula V equals one-third times capital B times h is shown.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1171505277171\">Since the base of a cone is a circle, we can substitute the formula of area of a circle, \\(\\pi{r}^{2}\\) , for \\(B\\) <em data-effect=\"italics\">to get the formula for volume of a cone.<\/em><\/p>\n<span id=\"fs-id2091497\" data-type=\"media\" data-alt=\"The formula V equals one-third times pi times r squared times h is shown.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_032_img.jpg\" alt=\"The formula V equals one-third times pi times r squared times h is shown.\" data-media-type=\"image\/jpeg\"><\/span>\n<p id=\"fs-id1171488303412\">In this book, we will only find the volume of a cone, and not its surface area.<\/p>\n\n<div class=\"textbox textbox--key-takeaways\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">Volume of a Cone<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1171499420872\">For a cone with radius \\(r\\) and height \\(h\\).<\/p>\n<span id=\"fs-id1171496323100\" data-type=\"media\" data-alt=\"An image of a cone is shown. The height is labeled h, the radius of the base is labeled r. Beside this is Volume: V equals one-third times pi times r squared times h.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_033_img.jpg\" alt=\"An image of a cone is shown. The height is labeled h, the radius of the base is labeled r. Beside this is Volume: V equals one-third times pi times r squared times h.\" data-media-type=\"image\/jpeg\"><\/span>\n\n<\/div>\n<\/div>\n<div id=\"fs-id1171487154931\" data-type=\"note\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1598937\" data-type=\"problem\">\n<p id=\"fs-id1598939\">Find the volume of a cone with height \\(6\\) inches and radius of its base \\(2\\) inches.<\/p>\n\n<\/div>\n<div id=\"fs-id1171505278364\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168467046430\" class=\"unnumbered unstyled\" summary=\"The text reads, \u201cStep 1. Read the problem.\u201d Beside this is an image of a cone. The radius is labeled 2, the height is labeled 6.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it\nwith the given information.<\/td>\n<td><span id=\"eip-id1168469795158\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_048_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the cone<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong>\nWrite the appropriate formula.\nSubstitute. (Use 3.14 for \\(\\pi \\))<\/td>\n<td>\\(V=\\frac{1}{3}\\phantom{\\rule{1em}{0ex}}\\pi \\phantom{\\rule{1.9em}{0ex}}{r}^{2}\\phantom{\\rule{1.7em}{0ex}}h\\)\n\\(V\\approx \\frac{1}{3}\\phantom{\\rule{0.7em}{0ex}}3.14\\phantom{\\rule{1em}{0ex}}{\\left(2\\right)}^{2}\\phantom{\\rule{1em}{0ex}}\\left(6\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td>\\(V\\approx 25.12\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> We leave it to you to check your\ncalculations.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume is approximately 25.12 cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171513623105\" data-type=\"problem\">\n<p id=\"fs-id1171513623107\">Find the volume of a cone with height \\(7\\) inches and radius \\(3\\) inches<\/p>\n\n<\/div>\n<div id=\"fs-id1935596\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1935598\">65.94 cu. in.<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1871880\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1476226\" data-type=\"exercise\">\n<div id=\"fs-id1171513623105\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1798404\" data-type=\"problem\">\n<p id=\"fs-id1171496945980\">Find the volume of a cone with height \\(9\\) centimetres and radius \\(5\\) centimetres<\/p>\n\n<\/div>\n<div id=\"fs-id1870007\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1573574\">235.5 cu. cm<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1759941\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1798402\" data-type=\"exercise\">\n<div id=\"fs-id1870007\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171505276418\" data-type=\"problem\">\n<p id=\"fs-id1759065\">Marty\u2019s favorite gastro pub serves french fries in a paper wrap shaped like a cone. What is the volume of a conic wrap that is \\(8\\) inches tall and \\(5\\) inches in diametre? Round the answer to the nearest hundredth.<\/p>\n\n<\/div>\n<div id=\"fs-id1571241\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168469874277\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information. Notice here that the base is the circle at the top of the cone.\u201d The word \u201cread\u201d is in bold. Beside this is an image of a cone. The diametre of the circle at the top of the cone is labeled 5. The height of the cone is labeled 8. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe volume of the cone.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet V equal volume.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute. (Use 3.14 for pi, and notice that we were given the distance across the circle, which is its diametre. The radius is 2.5 inches.)\u201d The word \u201ctranslate\u201d is in bold. Beside this is V equals one-third times pi times r squared times h. Below that is V is approximately one-third times 3.14 times 2.5 in. squared times 8 in. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is V is approximately 52.33. Step 6 says, \u201cCheck,\u201d in bold. Then \u201cWe leave it to you to check your arithmetic.\u201d Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe volume of the wrap is approximately 52.33 cubic inches.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information. Notice here that the base is the circle at the top of the cone.<\/td>\n<td><span id=\"eip-id1168466154518\" data-type=\"media\" data-alt=\".\"><img src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_049_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the cone<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong> Write the appropriate formula. Substitute. (Use 3.14 for \\(\\pi \\), and notice that we were given the distance across the circle, which is its diametre. The radius is 2.5 inches.)<\/td>\n<td>\\(V=\\frac{1}{3}\\phantom{\\rule{1em}{0ex}}\\pi \\phantom{\\rule{2.3em}{0ex}}{r}^{2}\\phantom{\\rule{2em}{0ex}}h\\)\n\\(V\\approx \\frac{1}{3}\\phantom{\\rule{0.7em}{0ex}}3.14\\phantom{\\rule{1em}{0ex}}{\\left(2.5\\right)}^{2}\\phantom{\\rule{1em}{0ex}}\\left(8\\right)\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td>\\(V\\approx 52.33\\)<\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> We leave it to you to check your calculations.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume of the wrap is approximately 52.33 cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171497994886\" data-type=\"problem\">\n<p id=\"fs-id1171497994888\">How many cubic inches of candy will fit in a cone-shaped pi\u00f1ata that is \\(18\\) inches long and \\(12\\) inches across its base? Round the answer to the nearest hundredth.<\/p>\n\n<\/div>\n<div id=\"fs-id1592722\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1592725\">678.24 cu. in.<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1903325\" data-type=\"problem\">\n<p id=\"fs-id1399880\">What is the volume of a cone-shaped party hat that is \\(10\\) inches tall and \\(7\\) inches across at the base? Round the answer to the nearest hundredth.<\/p>\n\n<\/div>\n<div id=\"fs-id1787346\" data-type=\"solution\"><details open=\"open\"><summary>Show answer<\/summary>\n<p id=\"fs-id1787349\">128.2 cu. in.<\/p>\n\n<\/details><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171505925375\" class=\"media-2\" data-type=\"note\">\n<div data-type=\"title\">ACCESS ADDITIONAL ONLINE RESOURCES<\/div>\n<ul id=\"fs-id1171498402192\">\n \t<li><a href=\"http:\/\/openstaxcollege.org\/l\/24volcone\">Volume of a Cone<\/a><\/li>\n<\/ul>\n<h1 data-type=\"title\">Key Concepts<\/h1>\n<ul id=\"eip-100\">\n \t<li><strong>Volume and Surface Area of a Rectangular Solid<\/strong>\n<ul id=\"eip-id3755293\">\n \t<li>\\(V=LWH\\)<\/li>\n \t<li>\\(S=2LH+2LW+2WH\\)<\/li>\n<\/ul>\n<\/li>\n \t<li><strong>Volume and Surface Area of a Cube<\/strong>\n<ul id=\"eip-id1171779023695\">\n \t<li>\\(V={s}^{3}\\)<\/li>\n \t<li>\\(S=6{s}^{2}\\)<\/li>\n<\/ul>\n<\/li>\n \t<li><strong>Volume and Surface Area of a Sphere<\/strong>\n<ul id=\"eip-id1171783978818\">\n \t<li>\\(V=\\frac{4}{3}\\pi {r}^{3}\\)<\/li>\n \t<li>\\(S=4\\pi {r}^{2}\\)<\/li>\n<\/ul>\n<\/li>\n \t<li><strong>Volume and Surface Area of a Cylinder<\/strong>\n<ul id=\"eip-id1171793481149\">\n \t<li>\\(V=\\pi {r}^{2}h\\)<\/li>\n \t<li>\\(S=2\\pi {r}^{2}+2\\pi rh\\)<\/li>\n<\/ul>\n<\/li>\n \t<li><strong>Volume of a Cone<\/strong>\n<ul id=\"eip-id1171782886821\">\n \t<li>For a cone with radius \\(r\\) and height \\(h\\):\nVolume: \\(V=\\frac{1}{3}\\pi {r}^{2}h\\)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id2063975\">\n \t<dt>cone<\/dt>\n \t<dd id=\"fs-id1171505120588\">A cone is a solid figure with one circular base and a vertex.<\/dd>\n<\/dl>\n<dl id=\"fs-id2036687\">\n \t<dt>cube<\/dt>\n \t<dd id=\"fs-id1417511\">A cube is a rectangular solid whose length, width, and height are equal.<\/dd>\n<\/dl>\n<dl id=\"fs-id1417515\">\n \t<dt>cylinder<\/dt>\n \t<dd id=\"fs-id1171487155088\">A cylinder is a solid figure with two parallel circles of the same size at the top and bottom.<\/dd>\n<\/dl>\n<\/div>\n<h1 data-type=\"title\">Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1614121\">Find Volume and Surface Area of Rectangular Solids<\/h2>\nIn the following exercises, find a) the volume and b) the surface area of the rectangular solid with the given dimensions.\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">1. length \\(2\\) metres, width \\(1.5\\) metres, height \\(3\\) metres<\/td>\n<td style=\"width: 50%;\">2. length \\(5\\) feet, width \\(8\\) feet, height \\(2.5\\) feet<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3. length \\(3.5\\) yards, width \\(2.1\\) yards, height \\(2.4\\) yards<\/td>\n<td style=\"width: 50%;\">4. length \\(8.8\\) centimetres, width \\(6.5\\) centimetres, height \\(4.2\\) centimetres<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1797305\">In the following exercises, solve.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">5.<strong data-effect=\"bold\"> Moving van<\/strong> A rectangular moving van has length \\(16\\) feet, width \\(8\\) feet, and height \\(8\\) feet. Find its a) volume and b) surface area.<\/td>\n<td style=\"width: 50%;\">6. <strong data-effect=\"bold\">Gift box<\/strong> A rectangular gift box has length \\(26\\) inches, width \\(16\\) inches, and height \\(4\\) inches. Find its a) volume and b) surface area.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">7.<strong data-effect=\"bold\"> Carton<\/strong> A rectangular carton has length \\(21.3\\) cm, width \\(24.2\\) cm, and height \\(6.5\\) cm. Find its a) volume and b) surface area.<\/td>\n<td style=\"width: 50%;\">8.<strong>Shipping container<\/strong> A rectangular shipping container has length \\(22.8\\) feet, width \\(8.5\\) feet, and height \\(8.2\\) feet. Find its a) volume and b) surface area.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1171505779653\">In the following exercises, find a) the volume and b) the surface area of the cube with the given side length.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">9. \\(5\\) centimetres<\/td>\n<td style=\"width: 50%;\">10. \\(6\\) inches<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">11. \\(10.4\\) feet<\/td>\n<td style=\"width: 50%;\">12. \\(12.5\\) metres<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id2238334\">In the following exercises, solve.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">13. <strong data-effect=\"bold\">Science center<\/strong> Each side of the cube at the Discovery Science Center in Santa Ana is \\(64\\) feet long. Find its a) volume and b) surface area.<\/td>\n<td style=\"width: 50%;\">14. <strong data-effect=\"bold\">Museum<\/strong> A cube-shaped museum has sides \\(45\\) metres long. Find its a) volume and b) surface area.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">15. <strong data-effect=\"bold\">Base of statue<\/strong> The base of a statue is a cube with sides \\(2.8\\) metres long. Find its a) volume and b) surface area.<\/td>\n<td style=\"width: 50%;\">16.<strong data-effect=\"bold\"> Tissue box<\/strong> A box of tissues is a cube with sides 4.5 inches long. Find its a) volume and b) surface area.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1171487568616\"><strong data-effect=\"bold\">\n<\/strong>Find the Volume and Surface Area of Spheres<\/h2>\n<p id=\"eip-236\">In the following exercises, find a) the volume and b) the surface area of the sphere with the given radius. Round answers to the nearest hundredth.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">17. \\(3\\) centimetres<\/td>\n<td style=\"width: 50%;\">18. \\(9\\) inches<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">19. \\(7.5\\) feet<\/td>\n<td style=\"width: 50%;\">20. \\(2.1\\) yards<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1171498398848\">In the following exercises, solve. Round answers to the nearest hundredth.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">21.<strong data-effect=\"bold\"> Exercise ball<\/strong> An exercise ball has a radius of \\(15\\) inches. Find its a) volume and b) surface area.<\/td>\n<td style=\"width: 50%;\">22. <strong data-effect=\"bold\">Balloon ride<\/strong> The Great Park Balloon is a big orange sphere with a radius of \\(36\\) feet . Find its a) volume and b) surface area.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">23. <strong data-effect=\"bold\">Golf ball<\/strong> A golf ball has a radius of \\(4.5\\) centimetres. Find its a) volume and b) surface area.<\/td>\n<td style=\"width: 50%;\">24.<strong data-effect=\"bold\"> Baseball<\/strong> A baseball has a radius of \\(2.9\\) inches. Find its a) volume and b) surface area.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1999562\"><strong data-effect=\"bold\">\n<\/strong>Find the Volume and Surface Area of a Cylinder<\/h2>\n<p id=\"eip-233\">In the following exercises, find a) the volume and b) the surface area of the cylinder with the given radius and height. Round answers to the nearest hundredth.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%; height: 56px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">25. radius \\(3\\) feet, height \\(9\\) feet<\/td>\n<td style=\"width: 50%; height: 14px;\">26. radius \\(5\\) centimetres, height \\(15\\) centimetres<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">27. radius \\(1.5\\) metres, height \\(4.2\\) metres<\/td>\n<td style=\"width: 50%; height: 14px;\">28. radius \\(1.3\\) yards, height \\(2.8\\) yards<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1171506675298\">In the following exercises, solve. Round answers to the nearest hundredth.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">29.<strong data-effect=\"bold\"> Coffee can<\/strong> A can of coffee has a radius of \\(5\\) cm and a height of \\(13\\) cm. Find its a) volume and b) surface area.<\/td>\n<td style=\"width: 50%;\">30.<strong data-effect=\"bold\"> Snack pack<\/strong> A snack pack of cookies is shaped like a cylinder with radius \\(4\\) cm and height \\(3\\) cm. Find its a) volume and b) surface area.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">31.<strong data-effect=\"bold\"> Barber shop pole<\/strong> A cylindrical barber shop pole has a diametre of \\(6\\) inches and height of \\(24\\) inches. Find its a) volume and b) surface area.<\/td>\n<td style=\"width: 50%;\">32. <strong data-effect=\"bold\">Architecture<\/strong> A cylindrical column has a diametre of \\(8\\) feet and a height of \\(28\\) feet. Find its a) volume and b) surface area.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1171505779470\"><strong data-effect=\"bold\">\n<\/strong>Find the Volume of Cones<\/h2>\nIn the following exercises, find the volume of the cone with the given dimensions. Round answers to the nearest hundredth.\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">33. height \\(9\\) feet and radius \\(2\\) feet<\/td>\n<td style=\"width: 50%;\">34. height \\(8\\) inches and radius \\(6\\) inches<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">35. height \\(12.4\\) centimetres and radius \\(5\\) cm<\/td>\n<td style=\"width: 50%;\">36. height \\(15.2\\) metres and radius \\(4\\) metres<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1563637\">In the following exercises, solve. Round answers to the nearest hundredth.<\/p>\n\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">37.<strong data-effect=\"bold\"> Teepee<\/strong> What is the volume of a cone-shaped teepee tent that is \\(10\\) feet tall and \\(10\\) feet across at the base?<\/td>\n<td style=\"width: 50%;\">38. <strong data-effect=\"bold\">Popcorn cup<\/strong> What is the volume of a cone-shaped popcorn cup that is \\(8\\) inches tall and \\(6\\) inches across at the base?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">39. <strong data-effect=\"bold\">Silo<\/strong> What is the volume of a cone-shaped silo that is \\(50\\) feet tall and \\(70\\) feet across at the base?<\/td>\n<td style=\"width: 50%;\">40. <strong data-effect=\"bold\">Sand pile<\/strong> What is the volume of a cone-shaped pile of sand that is \\(12\\) metres tall and \\(30\\) metres across at the base?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 style=\"text-align: left;\" data-type=\"title\">Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1171506170826\">41.<strong data-effect=\"bold\"> Street light post<\/strong> The post of a street light is shaped like a truncated cone, as shown in the picture below. It is a large cone minus a smaller top cone. The large cone is \\(30\\) feet tall with base radius \\(1\\) foot. The smaller cone is \\(10\\) feet tall with base radius of \\(0.5\\) feet. To the nearest tenth,<\/p>\n<p id=\"fs-id1591208\">a) find the volume of the large cone.<\/p>\n<p id=\"fs-id1591211\">b) find the volume of the small cone.<\/p>\n<p id=\"fs-id1171505984458\">c) find the volume of the post by subtracting the volume of the small cone from the volume of the large cone.<\/p>\n<span id=\"fs-id1691040\" data-type=\"media\" data-alt=\"An image of a cone is shown. There is a dark dotted line at the top indicating a smaller cone.\"><img class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_201_img.jpg\" alt=\"An image of a cone is shown. There is a dark dotted line at the top indicating a smaller cone.\" data-media-type=\"image\/jpeg\"><\/span><\/td>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1574935\">42. <strong data-effect=\"bold\">Ice cream cones<\/strong> A regular ice cream cone is 4 inches tall and has a diametre of \\(2.5\\) inches. A waffle cone is \\(7\\) inches tall and has a diametre of \\(3.25\\) inches. To the nearest hundredth,<\/p>\n<p id=\"fs-id1171498001417\">a) find the volume of the regular ice cream cone.<\/p>\n<p id=\"fs-id1758963\">b) find the volume of the waffle cone.<\/p>\n<p id=\"fs-id1758966\">c) how much more ice cream fits in the waffle cone compared to the regular cone?<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 style=\"text-align: left;\" data-type=\"title\">Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\" border=\"0\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">43. The formulas for the volume of a cylinder and a cone are similar. Explain how you can remember which formula goes with which shape.<\/td>\n<td style=\"width: 50%;\">44. Which has a larger volume, a cube of sides of \\(8\\) feet or a sphere with a diametre of \\(8\\) feet? Explain your reasoning.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1 style=\"text-align: left;\">Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%; height: 595px;\" border=\"0\">\n<tbody>\n<tr style=\"height: 103px;\">\n<td style=\"width: 33.3333%; height: 103px;\">1.\n\na) 9 cu. m\n\nb) 27 sq. m<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">3.\n\na) 17.64 cu. yd.\n\nb) 41.58 sq. yd.<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">5.\n\na) 1,024 cu. ft\n\nb) 640 sq. ft<\/td>\n<\/tr>\n<tr style=\"height: 103px;\">\n<td style=\"width: 33.3333%; height: 103px;\">7.\n<div id=\"fs-id1171497077335\" data-type=\"exercise\">\n<div id=\"fs-id1171506678898\" data-type=\"solution\">\n\na) 3,350.49 cu. cm\n\nb) 1,622.42 sq. cm\n\n<\/div>\n<\/div><\/td>\n<td style=\"width: 33.3333%; height: 103px;\">9.\n\na) 125 cu. cm\n\nb) 150 sq. cm<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">11.\n\na) 1124.864 cu. ft.\n\nb) 648.96 sq. ft<\/td>\n<\/tr>\n<tr style=\"height: 103px;\">\n<td style=\"width: 33.3333%; height: 103px;\">13.\n<div id=\"fs-id2238338\" data-type=\"exercise\">\n<div id=\"fs-id1864381\" data-type=\"solution\">\n\na) 262,144 cu. ft\n\nb) 24,576 sq. ft\n\n<\/div>\n<\/div><\/td>\n<td style=\"width: 33.3333%; height: 103px;\">15.\n<div id=\"fs-id1171513623124\" data-type=\"exercise\">\n<div id=\"fs-id1930588\" data-type=\"solution\">\n\na) 21.952 cu. m\n\nb) 47.04 sq. m\n\n<\/div>\n<\/div><\/td>\n<td style=\"width: 33.3333%; height: 103px;\">17.\n\na) 113.04 cu. cm\n\nb) 113.04 sq. cm<\/td>\n<\/tr>\n<tr style=\"height: 103px;\">\n<td style=\"width: 33.3333%; height: 103px;\">19.\n<div id=\"fs-id2024197\" data-type=\"exercise\">\n<div id=\"fs-id1555719\" data-type=\"solution\">\n\na) 1,766.25 cu. ft\n\nb) 706.5 sq. ft\n\n<\/div>\n<\/div><\/td>\n<td style=\"width: 33.3333%; height: 103px;\">21.\n\na) 14,130 cu. in.\n\nb) 2,826 sq. in.<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">23.\n\na) 381.51 cu. cm\n\nb) 254.34 sq. cm<\/td>\n<\/tr>\n<tr style=\"height: 103px;\">\n<td style=\"width: 33.3333%; height: 103px;\">25.\n\na) 254.34 cu. ft\n\nb) 226.08 sq. ft<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">27.\n\na) 29.673 cu. m\n\nb) 53.694 sq. m<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">29.\n\na) 1,020.5 cu. cm\n\nb) 565.2 sq. cm<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">31.\n\na) 678.24 cu. in.\n\nb) 508.68 sq. in.<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">33. 37.68 cu. ft<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">35. 324.47 cu. cm<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">37. 261.67 cu. ft<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">39. 64,108.33 cu. ft<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">41.\n\na) 31.4 cu. ft\n\nb) 2.6 cu. ft\n\nc) 28.8 cu. ft<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">43.\u00a0Answers will vary.<\/td>\n<td style=\"width: 33.3333%; height: 16px;\"><\/td>\n<td style=\"width: 33.3333%; height: 16px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<ul>\n \t<li>This chapter has been adapted from \u201cSolve Geometry Applications: Volume and Surface Area\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/li>\n<\/ul>","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Find volume and surface area of rectangular solids<\/li>\n<li>Find volume and surface area of spheres<\/li>\n<li>Find volume and surface area of cylinders<\/li>\n<li>Find volume of cone<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p id=\"fs-id1931140\">In this section, we will find the volume and surface area of some three-dimensional figures. Since we will be solving applications, we will once again show our Problem-Solving Strategy for Geometry Applications.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Problem Solving Strategy for Geometry Applications<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<ol class=\"stepwise\" type=\"1\">\n<li><strong data-effect=\"bold\">Read<\/strong> the problem and make sure you understand all the words and ideas. Draw the figure and label it with the given information.<\/li>\n<li><strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/li>\n<li><strong data-effect=\"bold\">Name<\/strong> what you are looking for. Choose a variable to represent that quantity.<\/li>\n<li><strong data-effect=\"bold\">Translate<\/strong> into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.<\/li>\n<li><strong data-effect=\"bold\">Solve<\/strong> the equation using good algebra techniques.<\/li>\n<li><strong data-effect=\"bold\">Check<\/strong> the answer in the problem and make sure it makes sense.<\/li>\n<li><strong data-effect=\"bold\">Answer<\/strong> the question with a complete sentence.<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Find Volume and Surface Area of Rectangular Solids<\/h1>\n<p>A cheer leading coach is having the squad paint wooden crates with the school colors to stand on at the games. (See <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_06_001\">Figure.1<\/a>). The amount of paint needed to cover the outside of each box is the surface area, a square measure of the total area of all the sides. The amount of space inside the crate is the volume, a cubic measure.<\/p>\n<div id=\"CNX_BMath_Figure_09_06_001\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">This wooden crate is in the shape of a rectangular solid.<\/div>\n<figure style=\"width: 374px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2020\/08\/CNX_BMath_Figure_09_06_001.jpg\" alt=\"This is an image of a wooden crate.\" width=\"374\" height=\"227\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure.1<\/figcaption><\/figure>\n<p id=\"fs-id1475627\">Each crate is in the shape of a rectangular solid. Its dimensions are the length, width, and height. The rectangular solid shown in <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_06_002\">Figure.2<\/a> has length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/> units, width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> units, and height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> units. Can you tell how many cubic units there are altogether? Let\u2019s look layer by layer.<\/p>\n<p>Breaking a rectangular solid into layers makes it easier to visualize the number of cubic units it contains. This <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/> by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> by <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> rectangular solid has <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-762747d84dc941b4e4b85f0d3d4eb09e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> cubic units.<\/p>\n<div id=\"CNX_BMath_Figure_09_06_002\" class=\"bc-figure figure\">\n<figure style=\"width: 507px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_002.jpg\" alt=\"A rectangular solid is shown. Each layer is composed of 8 cubes, measuring 2 by 4. The top layer is pink. The middle layer is orange. The bottom layer is green. Beside this is an image of the top layer that says \u201cThe top layer has 8 cubic units.\u201d The orange layer is shown and says \u201cThe middle layer has 8 cubic units.\u201d The green layer is shown and says, \u201cThe bottom layer has 8 cubic units.\u201d\" width=\"507\" height=\"133\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure.2<\/figcaption><\/figure>\n<p id=\"fs-id1171487599067\">Altogether there are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-762747d84dc941b4e4b85f0d3d4eb09e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> cubic units. Notice that <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-762747d84dc941b4e4b85f0d3d4eb09e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> is the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a61bf40e72a3312ece0c64ea4ef536ef_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#108;&#101;&#110;&#103;&#116;&#104;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#48;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#48;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#105;&#100;&#116;&#104;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#48;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#48;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#104;&#101;&#105;&#103;&#104;&#116;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"259\" style=\"vertical-align: -4px;\" \/><\/p>\n<p><span id=\"fs-id1171498001442\" data-type=\"media\" data-alt=\"The top line says V equals L times W times H. Beneath the V is 24, beneath the equal sign is another equal sign, beneath the L is a 4, beneath the W is a 2, beneath the H is a 3.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_002_img.jpg\" alt=\"The top line says V equals L times W times H. Beneath the V is 24, beneath the equal sign is another equal sign, beneath the L is a 4, beneath the W is a 2, beneath the H is a 3.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1171505120230\"><strong>The volume, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-63ada879859a9e41fd935f035b7313bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>, of any rectangular solid is the product of the length, width, and height.<\/strong><\/p>\n<p><strong><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-70441d53f3f0f6969e5be735ccb8b3f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#76;&#87;&#72;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"85\" style=\"vertical-align: 0px;\" \/><\/strong><\/p>\n<p id=\"fs-id1171488252104\">We could also write the formula for volume of a rectangular solid in terms of the area of the base. The area of the base, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#66;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>, is equal to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-68956675929e485f0b447c9afeb4380b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#108;&#101;&#110;&#103;&#116;&#104;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#116;&#101;&#120;&#116;&#123;&#119;&#105;&#100;&#116;&#104;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#46;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"118\" style=\"vertical-align: -4px;\" \/><\/p>\n<div id=\"fs-id1171104062309\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-da412ea06a388c9c40788d1e092c5815_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#66;&#125;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#76;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#116;&#101;&#120;&#116;&#123;&#87;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"78\" style=\"vertical-align: 0px;\" \/><\/div>\n<p id=\"fs-id1793392\">We can substitute <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-92d94f2b1c3e25a4fdd5e7615e340179_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#66;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\" \/> for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-14fac04c525614aeac1462d1b2679c41_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#76;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#116;&#101;&#120;&#116;&#123;&#87;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: 0px;\" \/> in the volume formula to get another form of the volume formula.<\/p>\n<p><span id=\"fs-id1171506203641\" data-type=\"media\" data-alt=\"The top line says V equals red L times red W times H. Below this is V equals red parentheses L times W times H. Below this is V equals red capital B times h.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_003_img.jpg\" alt=\"The top line says V equals red L times red W times H. Below this is V equals red parentheses L times W times H. Below this is V equals red capital B times h.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1933170\">We now have another version of the volume formula for rectangular solids. Let\u2019s see how this works with the <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-242908cd047da1cba03f27dc1d326c64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#105;&#109;&#101;&#115;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"84\" style=\"vertical-align: 0px;\" \/> rectangular solid we started with. See <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_06_004\">Figure.3<\/a>.<\/p>\n<div id=\"CNX_BMath_Figure_09_06_004\" class=\"bc-figure figure\">\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_004_img.jpg\" alt=\"An image of a rectangular solid is shown. It is made up of cubes. It is labeled as 2 by 4 by 3. Beside the solid is V equals Bh. Below this is V equals Base times height. Below Base is parentheses 4 times 2. The next line says V equals parentheses 4 times 2 times 3. Below that is V equals 8 times 3, then V equals 24 cubic units.\" width=\"302\" height=\"118\" data-media-type=\"image\/jpeg\" \/><\/p>\n<h3>Figure.3<\/h3>\n<\/div>\n<p id=\"fs-id1171505368262\">To find the <em data-effect=\"italics\">surface area<\/em> of a rectangular solid, think about finding the area of each of its faces. How many faces does the rectangular solid above have? You can see three of them.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c9a76f5d58630e920710e9021bce2d53_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#99;&#99;&#125;&#123;&#65;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#114;&#111;&#110;&#116;&#125;&#125;&#61;&#76;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#87;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#65;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#105;&#100;&#101;&#125;&#125;&#61;&#76;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#87;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#65;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#111;&#112;&#125;&#125;&#61;&#76;&#92;&#116;&#105;&#109;&#101;&#115;&#32;&#87;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#123;&#65;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#114;&#111;&#110;&#116;&#125;&#125;&#61;&#52;&#92;&#99;&#100;&#111;&#116;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#65;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#105;&#100;&#101;&#125;&#125;&#61;&#50;&#92;&#99;&#100;&#111;&#116;&#51;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#65;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#111;&#112;&#125;&#125;&#61;&#52;&#92;&#99;&#100;&#111;&#116;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#123;&#65;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#114;&#111;&#110;&#116;&#125;&#125;&#61;&#49;&#50;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#65;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#105;&#100;&#101;&#125;&#125;&#61;&#54;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#123;&#65;&#125;&#95;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#111;&#112;&#125;&#125;&#61;&#56;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"63\" width=\"441\" style=\"vertical-align: -28px;\" \/><\/p>\n<p>Notice for each of the three faces you see, there is an identical opposite face that does not show.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b8fc086bdce697a4400f6300431c2845_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#108;&#125;&#83;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#114;&#111;&#110;&#116;&#125;&#43;&#92;&#116;&#101;&#120;&#116;&#123;&#98;&#97;&#99;&#107;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#116;&#101;&#120;&#116;&#123;&#43;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#108;&#101;&#102;&#116;&#32;&#115;&#105;&#100;&#101;&#125;&#43;&#92;&#116;&#101;&#120;&#116;&#123;&#114;&#105;&#103;&#104;&#116;&#32;&#115;&#105;&#100;&#101;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#111;&#112;&#125;&#43;&#92;&#116;&#101;&#120;&#116;&#123;&#98;&#111;&#116;&#116;&#111;&#109;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#83;&#61;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#99;&#100;&#111;&#116;&#92;&#116;&#101;&#120;&#116;&#123;&#102;&#114;&#111;&#110;&#116;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#116;&#101;&#120;&#116;&#123;&#108;&#101;&#102;&#116;&#32;&#115;&#105;&#100;&#101;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#92;&#108;&#101;&#102;&#116;&#40;&#92;&#116;&#101;&#120;&#116;&#123;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#116;&#101;&#120;&#116;&#123;&#116;&#111;&#112;&#125;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#92;&#32;&#83;&#61;&#50;&#92;&#99;&#100;&#111;&#116;&#49;&#50;&#43;&#50;&#92;&#99;&#100;&#111;&#116;&#54;&#43;&#50;&#92;&#99;&#100;&#111;&#116;&#56;&#92;&#92;&#32;&#83;&#61;&#50;&#52;&#43;&#49;&#50;&#43;&#49;&#54;&#92;&#92;&#32;&#83;&#61;&#53;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#113;&#46;&#32;&#117;&#110;&#105;&#116;&#115;&#125;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"106\" width=\"471\" style=\"vertical-align: -48px;\" \/><\/p>\n<p id=\"fs-id1418671\">The surface area <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-520cb534cd5b6bed768a61515b57cb7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\" \/> of the rectangular solid shown in <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_06_004\">(Figure.3)<\/a> is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-30352d66e4a511eedaaaf1c7497a30c9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> square units.<\/p>\n<p>In general, to find the surface area of a rectangular solid, remember that each face is a rectangle, so its area is the product of its length and its width (see <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_06_005\">Figure.4<\/a>). Find the area of each face that you see and then multiply each area by two to account for the face on the opposite side.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-87093e0b1202288d622c31bdb6c49782_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#50;&#76;&#72;&#43;&#50;&#76;&#87;&#43;&#50;&#87;&#72;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"200\" style=\"vertical-align: -2px;\" \/><\/p>\n<p>For each face of the rectangular solid facing you, there is another face on the opposite side. There are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> faces in all.<\/p>\n<div id=\"CNX_BMath_Figure_09_06_005\" class=\"bc-figure figure\">\n<figure style=\"width: 156px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_005.jpg\" alt=\"A rectangular solid is shown. The sides are labeled L, W, and H. One face is labeled LW and another is labeled WH.\" width=\"156\" height=\"173\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure.4<\/figcaption><\/figure>\n<div id=\"fs-id1658379\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Volume and Surface Area of a Rectangular Solid<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>For a rectangular solid with length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-66a9f474fc3c52efdfb0ba6a70199ee8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#76;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\" \/>, width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4caed22919a1780df1b6310b338b904e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#87;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/>, and height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b2b40462f73b4b119efc19d50a3580b1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#72;&#58;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"25\" style=\"vertical-align: 0px;\" \/><\/p>\n<p><span id=\"fs-id1686239\" data-type=\"media\" data-alt=\"A rectangular solid is shown. The sides are labeled L, W, and H. Beside it is Volume: V equals LWH equals BH. Below that is Surface Area: S equals 2LH plus 2LW plus 2WH.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_006_img.jpg\" alt=\"A rectangular solid is shown. The sides are labeled L, W, and H. Beside it is Volume: V equals LWH equals BH. Below that is Surface Area: S equals 2LH plus 2LW plus 2WH.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div data-type=\"note\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div data-type=\"problem\">\n<p id=\"fs-id1178399\">For a rectangular solid with length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38826cadfc5dbf2d92abbbfd6d370410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> cm, height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b976c8c10558ac50c42d953f3ee38707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -1px;\" \/> cm, and width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> cm, find the a) volume and b) surface area.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1594850\">Step 1 is the same for both a) and b), so we will show it just once.<\/p>\n<table id=\"eip-id1168468779989\" class=\"unnumbered unstyled\" summary=\"The text reads, \u201cStep 1. Read the problem. Draw the figure and label it with the given information.\u201d Beside this is an image of a rectangular solid. It is labeled 14 by 9 by 17.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and<br \/>\nlabel it with the given information.<\/td>\n<td><span id=\"eip-id1168468780014\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_038_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468454551\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the rectangular solid<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-63ada879859a9e41fd935f035b7313bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>= volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-70441d53f3f0f6969e5be735ccb8b3f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#76;&#87;&#72;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"85\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3c29c52994236b9c1d408592c4868bbe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#92;&#109;&#97;&#116;&#104;&#114;&#109;&#123;&#49;&#52;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#57;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"108\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b763ce2bd8fa0b7c94dcb12d42da24d6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#50;&#44;&#49;&#52;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"81\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check<\/strong><br \/>\nWe leave it to you to check your calculations.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The surface area is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6af1514a676fbf3ab775a2132c393b28_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#116;&#101;&#120;&#116;&#123;&#49;&#44;&#48;&#51;&#52;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"40\" style=\"vertical-align: -4px;\" \/> square centimetres.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168469477419\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the surface area of the solid<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>Let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-520cb534cd5b6bed768a61515b57cb7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\" \/>= surface area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-87093e0b1202288d622c31bdb6c49782_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#50;&#76;&#72;&#43;&#50;&#76;&#87;&#43;&#50;&#87;&#72;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"200\" style=\"vertical-align: -2px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fbba2c1d377d370a394e78790ecb0c1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#49;&#52;&#92;&#99;&#100;&#111;&#116;&#32;&#57;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#57;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#55;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"282\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve the equation.<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e66dab2bbfdcf11ca0b717847d2b55e0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#49;&#44;&#48;&#51;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"79\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Double-check with a calculator.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The surface area is 1,034 square centimetres.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1658281\" data-type=\"problem\">\n<p id=\"fs-id1406524\">Find the a) volume and b) surface area of rectangular solid with the: length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet, width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet, and height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cba90047eec6a05e400b16dfb86d7f29_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> feet.<\/p>\n<\/div>\n<div id=\"fs-id1171506137807\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168466313772\" class=\"circled\" type=\"a\">\n<li>792 cu. ft<\/li>\n<li>518 sq. ft<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1171505624033\" data-type=\"exercise\">\n<div id=\"fs-id1658281\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 1.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1563070\" data-type=\"problem\">\n<p id=\"fs-id1171505480381\">Find the a) volume and b) surface area of rectangular solid with the: length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b59223d2c162a0fdd163af8597f0845e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -1px;\" \/> feet, width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-40f7428479801bf4ef27a5149e9df526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> feet, and height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet.<\/p>\n<\/div>\n<div id=\"fs-id1932667\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168466312554\" class=\"circled\" type=\"a\">\n<li>1,440 cu. ft<\/li>\n<li>792 sq. ft<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1602274\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1171516922529\" data-type=\"exercise\">\n<div id=\"fs-id1563070\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171498355737\" data-type=\"problem\">\n<p>A rectangular crate has a length of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-874b63beceda768488ea76f12b9cf9e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> inches, width of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dd40a7f142c1fc4152e724db5432f76b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: 0px;\" \/> inches, and height of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-930d01a5f622cee5952bab4752e56063_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> inches. Find its a) volume and b) surface area.<\/p>\n<\/div>\n<div id=\"fs-id1592712\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1528864\">Step 1 is the same for both a) and b), so we will show it just once.<\/p>\n<table id=\"eip-id1168467275051\" class=\"unnumbered unstyled\" summary=\"The text reads, \u201cStep 1. Read the problem. Draw the figure and label it with the given information.\u201d Beside this is an image of a rectangular solid. It is labeled 30 by 25 by 20.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and<br \/>\nlabel it with the given information.<\/td>\n<td><span id=\"eip-id1168468779962\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_039_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467238054\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the crate<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-63ada879859a9e41fd935f035b7313bc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>= volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-70441d53f3f0f6969e5be735ccb8b3f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#76;&#87;&#72;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"85\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b8405bfe5bba304758f153d8ff806ef0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#51;&#48;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#53;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"117\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-221168acd1a09988cc8108f6b261b9d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#49;&#53;&#44;&#48;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"91\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Double check your math.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume is 15,000 cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467505864\" class=\"unnumbered unstyled\" style=\"height: 130px;\" summary=\".\" data-label=\"\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 290.406px;\">b)<\/td>\n<td style=\"height: 14px; width: 469.406px;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 290.406px;\">Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td style=\"height: 14px; width: 469.406px;\">the surface area of the crate<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 290.406px;\">Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td style=\"height: 14px; width: 469.406px;\">let <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-520cb534cd5b6bed768a61515b57cb7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\" \/>= surface area<\/td>\n<\/tr>\n<tr style=\"height: 46px;\">\n<td style=\"height: 46px; width: 290.406px;\">Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute.<\/td>\n<td style=\"height: 46px; width: 469.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-87093e0b1202288d622c31bdb6c49782_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#50;&#76;&#72;&#43;&#50;&#76;&#87;&#43;&#50;&#87;&#72;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"200\" style=\"vertical-align: -2px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-9a3f68b8b7dcb673164641030a3de62f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#48;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#48;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#43;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#53;&#92;&#99;&#100;&#111;&#116;&#32;&#50;&#48;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"300\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 290.406px;\">Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td style=\"height: 14px; width: 469.406px;\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1dff0219e1e1c008b9fc1e0b64747177_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#51;&#44;&#55;&#48;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"79\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 290.406px;\">Step 6. <strong data-effect=\"bold\">Check:<\/strong> Check it yourself!<\/td>\n<td style=\"height: 14px; width: 469.406px;\"><\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"height: 14px; width: 290.406px;\">Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td style=\"height: 14px; width: 469.406px;\">The surface area is 3,700 square inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1394700\" data-type=\"problem\">\n<p>A rectangular box has length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet, width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/> feet, and height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet. Find its a) volume and b) surface area.<\/p>\n<\/div>\n<div id=\"fs-id1171505547241\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168468373746\" class=\"circled\" type=\"a\">\n<li>216 cu. ft<\/li>\n<li>228 sq. ft<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1762464\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2064891\" data-type=\"exercise\">\n<div id=\"fs-id1171505547241\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 2.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1608864\" data-type=\"problem\">\n<p id=\"fs-id1171506673948\">A rectangular suitcase has length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-01cb55a185cee9b8f0aa311ce70a4b82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"17\" style=\"vertical-align: 0px;\" \/> inches, width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38826cadfc5dbf2d92abbbfd6d370410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> inches, and height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches. Find its a) volume and b) surface area.<\/p>\n<\/div>\n<div id=\"fs-id1171506207477\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168469802778\" class=\"circled\" type=\"a\">\n<li>2,772 cu. in.<\/li>\n<li>1,264 sq. in.<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1 data-type=\"title\">Volume and Surface Area of a Cube<\/h1>\n<p id=\"fs-id1171505481979\">A cube is a rectangular solid whose length, width, and height are equal. See Volume and Surface Area of a Cube, below. Substituting, <em data-effect=\"italics\">s<\/em> for the length, width and height into the formulas for volume and surface area of a rectangular solid, we get:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fe52ee4ff94040749ac3fa4744024ea8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#97;&#114;&#114;&#97;&#121;&#125;&#123;&#99;&#99;&#99;&#99;&#99;&#125;&#86;&#61;&#76;&#87;&#72;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#83;&#61;&#50;&#76;&#72;&#43;&#50;&#76;&#87;&#43;&#50;&#87;&#72;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#86;&#61;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#83;&#61;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#43;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#43;&#50;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#92;&#99;&#100;&#111;&#116;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#86;&#61;&#123;&#92;&#116;&#101;&#120;&#116;&#123;&#115;&#125;&#125;&#94;&#123;&#51;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#83;&#61;&#50;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#92;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#38;&#32;&#83;&#61;&#54;&#123;&#115;&#125;&#94;&#123;&#50;&#125;&#92;&#104;&#102;&#105;&#108;&#108;&#32;&#92;&#101;&#110;&#100;&#123;&#97;&#114;&#114;&#97;&#121;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"78\" width=\"350\" style=\"vertical-align: -33px;\" \/><\/p>\n<p id=\"fs-id1767806\">So for a cube, the formulas for volume and surface area are <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-edc9b90cd61abac690fd07c160d33677_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#123;&#115;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"53\" style=\"vertical-align: 0px;\" \/> and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e7cdf899a512101dcb9bdc85022f87c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#54;&#123;&#115;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<div id=\"fs-id1560075\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Volume and Surface Area of a Cube<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1516282\">For any cube with sides of length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ae1901659f469e6be883797bfd30f4f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#115;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/>,<\/p>\n<p><span id=\"fs-id1171496258265\" data-type=\"media\" data-alt=\"An image of a cube is shown. Each side is labeled s. Beside this is Volume: V equals s cubed. Below that is Surface Area: S equals 6 times s squared.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_010_img.jpg\" alt=\"An image of a cube is shown. Each side is labeled s. Beside this is Volume: V equals s cubed. Below that is Surface Area: S equals 6 times s squared.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 3<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171496189268\" data-type=\"problem\">\n<p id=\"fs-id1171505620889\">A cube is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-01948ea56b434f27f412043e785fe880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> inches on each side. Find its a) volume and b) surface area.<\/p>\n<\/div>\n<div id=\"fs-id1585408\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1784097\">Step 1 is the same for both a) and b), so we will show it just once.<\/p>\n<table id=\"eip-id1168466154480\" class=\"unnumbered unstyled\" summary=\"The text reads, \u201cStep 1. Read the problem. Draw the figure and label it with the given information.\u201d Beside this is an image of a cube. It is labeled 2.5 by 2.5 by 2.5.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and<br \/>\nlabel it with the given information.<\/td>\n<td><span id=\"eip-id1168469766852\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_040_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168465993815\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the cube<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-edc9b90cd61abac690fd07c160d33677_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#123;&#115;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"53\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong> Substitute and solve.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a619c720937dde578e517323cbc961de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#46;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"81\" style=\"vertical-align: -4px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7d276019cf15220de9d28d2000f01048_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#49;&#53;&#46;&#54;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"87\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Check your work.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume is 15.625 cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168466275896\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the surface area of the cube<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">S<\/em> = surface area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e7cdf899a512101dcb9bdc85022f87c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#54;&#123;&#115;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong> Substitute and solve.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3f584c03750ef76028c874d7fdb4646f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#54;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#46;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"101\" style=\"vertical-align: -4px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6d70a69ededf39b23cfc9a38bf016b0d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#51;&#55;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"67\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> The check is left to you.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The surface area is 37.5 square inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1489297\" data-type=\"problem\">\n<p id=\"fs-id1529247\">For a cube with side 4.5 metres, find the a) volume and b) surface area of the cube.<\/p>\n<\/div>\n<div id=\"fs-id1933234\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168466248223\" class=\"circled\" type=\"a\">\n<li>91.125 cu. m<\/li>\n<li>121.5 sq. m<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"try\" data-type=\"note\">\n<div id=\"fs-id1452349\" data-type=\"exercise\">\n<div id=\"fs-id1489297\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 3.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171487571769\" data-type=\"problem\">\n<p>For a cube with side 7.3 yards, find the a) volume and b) surface area of the cube.<\/p>\n<\/div>\n<div id=\"fs-id1529140\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168467222372\" class=\"circled\" type=\"a\">\n<li>389.017 cu. yd.<\/li>\n<li>319.74 sq. yd.<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1590812\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1418268\" data-type=\"exercise\">\n<div id=\"fs-id1171487571769\" data-type=\"problem\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 4<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171506138160\" data-type=\"problem\">\n<p id=\"fs-id1171505934498\">A notepad cube measures <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> inches on each side. Find its a) volume and b) surface area.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168467296950\" class=\"unnumbered unstyled\" summary=\"The text reads, \u201cStep 1. Read the problem. Draw the figure and label it with the given information.\u201d Beside this is an image of a cube. It is labeled 2 by 2 by 2.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and<br \/>\nlabel it with the given information.<\/td>\n<td><span id=\"eip-id1168467496838\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_041_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467188434\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the cube<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-edc9b90cd61abac690fd07c160d33677_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#123;&#115;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"53\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0d786f11e2d8f73bb49592bae354f7b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#123;&#50;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"54\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f376b6f7054c6baa0905cae4d0c5c48e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Check that you did the calculations<br \/>\ncorrectly.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume is 8 cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468478236\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the surface area of the cube<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">S<\/em> = surface area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e7cdf899a512101dcb9bdc85022f87c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#54;&#123;&#115;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve<\/strong> the equation.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-bc026354a09a69cc872a4927311b0ab7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#54;&#92;&#99;&#100;&#111;&#116;&#32;&#123;&#50;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"73\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-685c7151adb58b7b872e79b47c524bf2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"54\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> The check is left to you.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The surface area is 24 square inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1927378\" data-type=\"problem\">\n<p id=\"fs-id1871924\">A packing box is a cube measuring <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/> feet on each side. Find its a) volume and b) surface area.<\/p>\n<\/div>\n<div id=\"fs-id1171511527503\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168466072253\" class=\"circled\" type=\"a\">\n<li>64 cu. ft<\/li>\n<li>96 sq. ft<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1038661\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2058174\" data-type=\"exercise\">\n<div id=\"fs-id1171511527503\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 4.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1927378\" data-type=\"problem\">\n<p id=\"fs-id1871924\">A packing box is a cube measuring <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/> feet on each side. Find its a) volume and b) surface area.<\/p>\n<\/div>\n<div id=\"fs-id1171511527503\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168466072253\" class=\"circled\" type=\"a\">\n<li>64 cu. ft<\/li>\n<li>96 sq. ft<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Find the Volume and Surface Area of Spheres<\/h1>\n<p id=\"fs-id1954343\">A sphere is the shape of a basketball, like a three-dimensional circle. Just like a circle, the size of a sphere is determined by its radius, which is the distance from the centre of the sphere to any point on its surface. The formulas for the volume and surface area of a sphere are given below.<\/p>\n<p id=\"eip-745\">Showing where these formulas come from, like we did for a rectangular solid, is beyond the scope of this course. We will approximate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/> with <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-980f77b67737a79200c69c26bf9f365c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"32\" style=\"vertical-align: -1px;\" \/>.<\/p>\n<div id=\"fs-id1171512117057\" data-type=\"note\">\n<div data-type=\"title\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Volume and Surface Area of a Sphere<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1171512117850\">For a sphere with radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f712f0944335b41e5bfeb84febf17f27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;&#92;&#116;&#101;&#120;&#116;&#123;&#58;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"12\" style=\"vertical-align: 0px;\" \/><\/p>\n<p><span id=\"fs-id1171505277582\" data-type=\"media\" data-alt=\"An image of a sphere is shown. The radius is labeled r. Beside this is Volume: V equals four-thirds times pi times r cubed. Below that is Surface Area: S equals 4 times pi times r squared.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_015.jpg\" alt=\"An image of a sphere is shown. The radius is labeled r. Beside this is Volume: V equals four-thirds times pi times r cubed. Below that is Surface Area: S equals 4 times pi times r squared.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 5<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171498454044\" data-type=\"problem\">\n<p id=\"fs-id1171498401975\">A sphere has a radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches. Find its a) volume and b) surface area.<\/p>\n<\/div>\n<div id=\"fs-id1650050\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<div data-type=\"title\"><\/div>\n<p id=\"fs-id1171512511594\">Step 1 is the same for both a) and b), so we will show it just once.<\/p>\n<table id=\"eip-id1168468504255\" class=\"unnumbered unstyled\" summary=\"The text reads, \u201cStep 1. Read the problem. Draw the figure and label it with the given information.\u201d Beside this is an image of a sphere. The radius is labeled 6.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label<br \/>\nit with the given information.<\/td>\n<td><span id=\"eip-id1168468504279\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_042_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168466046693\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the sphere<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7c7e25a744b15835f98879ff2be16df7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-47117201447fb5bbe61ff235596c3161_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#54;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"116\" style=\"vertical-align: -6px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-232cc8d89929a2db3655c6fbcaf38d9e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#57;&#48;&#52;&#46;&#51;&#50;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#116;&#101;&#120;&#116;&#123;&#99;&#117;&#98;&#105;&#99;&#32;&#105;&#110;&#99;&#104;&#101;&#115;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"184\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Double-check your math on a calculator.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume is approximately 904.32 cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467263246\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the surface area of the cube<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">S<\/em> = surface area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cef1f49eebfcd3582a52a057f75f77a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#52;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"71\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7528e0026a5257ca5bf0e49a9cd354a9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#54;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"112\" style=\"vertical-align: -4px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-af9daf4cff136e2e88f8c8356d87c20a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#52;&#53;&#50;&#46;&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"86\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> Double-check your math on a calculator<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The surface area is approximately 452.16 square inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1913002\" data-type=\"problem\">\n<p id=\"fs-id1171488074403\">Find the a) volume and b) surface area of a sphere with radius 3 centimetres.<\/p>\n<\/div>\n<div data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168466006411\" class=\"circled\" type=\"a\">\n<li>113.04 cu. cm<\/li>\n<li>113.04 sq. cm<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171506644186\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id2091579\" data-type=\"exercise\">\n<div data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 5.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171505891413\" data-type=\"problem\">\n<p id=\"fs-id1574560\">Find the a) volume and b) surface area of each sphere with a radius of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> foot<\/p>\n<\/div>\n<div id=\"fs-id748315\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168467234126\" class=\"circled\" type=\"a\">\n<li>4.19 cu. ft<\/li>\n<li>12.56 sq. ft<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171498000511\" class=\"try\" data-type=\"note\">\n<div data-type=\"exercise\">\n<div id=\"fs-id748315\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 6<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id945308\" data-type=\"problem\">\n<p id=\"fs-id1566505\">A globe of Earth is in the shape of a sphere with radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-38826cadfc5dbf2d92abbbfd6d370410_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> centimetres. Find its a) volume and b) surface area. Round the answer to the nearest hundredth.<\/p>\n<\/div>\n<div id=\"fs-id1171488252639\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168467368787\" class=\"unnumbered unstyled\" summary=\"Step 1. Read the problem.\u201d Beside this is an image of a globe. The radius is labeled 14.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw a figure with the<br \/>\ngiven information and label it.<\/td>\n<td><span id=\"eip-id1168467309173\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_043_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168464926516\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the sphere<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute. (Use 3.14 for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7c7e25a744b15835f98879ff2be16df7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e0632b43fd5e828b2088fdea44f0cd03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#49;&#52;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"125\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f331cc81c0f608896a4caf8206f56846_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#49;&#49;&#44;&#52;&#56;&#56;&#46;&#50;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"113\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> We leave it to you to check your calculations.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume is approximately 11,488.21 cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468466725\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the surface area of the sphere<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">S<\/em> = surface area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute. (Use 3.14 for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cef1f49eebfcd3582a52a057f75f77a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#52;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"71\" style=\"vertical-align: -1px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f262fde23f978280f04369b8ab9ff275_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#52;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#49;&#52;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"120\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f559e685ed3e244a28bc7f109d72173b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#50;&#52;&#54;&#49;&#46;&#55;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"95\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> We leave it to you to check your calculations.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The surface area is approximately 2461.76 square inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1561201\" data-type=\"problem\">\n<p id=\"fs-id1398847\">A beach ball is in the shape of a sphere with radius of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches. Find its a) volume and b) surface area.<\/p>\n<\/div>\n<div id=\"fs-id1531978\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168468772882\" class=\"circled\" type=\"a\">\n<li>3052.08 cu. in.<\/li>\n<li>1017.36 sq. in.<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1418575\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1398911\" data-type=\"exercise\">\n<div id=\"fs-id1531978\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 6.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1552724\" data-type=\"problem\">\n<p id=\"fs-id1171505276108\">A Roman statue depicts Atlas holding a globe with radius of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2b2514947ef7a7471f9fcd9c60117cf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"21\" style=\"vertical-align: -1px;\" \/> feet. Find the a) volume and b) surface area of the globe.<\/p>\n<\/div>\n<div id=\"fs-id1171511528462\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168467200300\" class=\"circled\" type=\"a\">\n<li>14.13 cu. ft<\/li>\n<li>28.26 sq. ft<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Find the Volume and Surface Area of a Cylinder<\/h1>\n<p id=\"fs-id1804291\">If you have ever seen a can of soda, you know what a cylinder looks like. A cylinder is a solid figure with two parallel circles of the same size at the top and bottom. The top and bottom of a cylinder are called the bases. The height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-14b463d0ecd5b350ced6cf1d6a12eef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\" \/> of a cylinder is the distance between the two bases. For all the cylinders we will work with here, the sides and the height, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-14b463d0ecd5b350ced6cf1d6a12eef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\" \/> , will be perpendicular to the bases.<\/p>\n<p>A cylinder has two circular bases of equal size. The height is the distance between the bases.<\/p>\n<div id=\"CNX_BMath_Figure_09_06_020\" class=\"bc-figure figure\">\n<p><span id=\"fs-id1777988\" data-type=\"media\" data-alt=\"An image of a cylinder is shown. There is a red arrow pointing to the radius of the top labeling it r, radius. There is a red arrow pointing to the height of the cylinder labeling it h, height.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_020_img.jpg\" alt=\"An image of a cylinder is shown. There is a red arrow pointing to the radius of the top labeling it r, radius. There is a red arrow pointing to the height of the cylinder labeling it h, height.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p id=\"fs-id1772153\">Rectangular solids and cylinders are somewhat similar because they both have two bases and a height. The formula for the volume of a rectangular solid, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-afa19cbce8e213b53250f325166fa39f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#66;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"62\" style=\"vertical-align: 0px;\" \/> , can also be used to find the volume of a cylinder.<\/p>\n<p id=\"fs-id1748732\">For the rectangular solid, the area of the base, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#66;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/> , is the area of the rectangular base, length \u00d7 width. For a cylinder, the area of the base, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#66;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/>, is the area of its circular base, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-58f98c23a919bbe15f71547e3eb39279_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/>. <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_06_021\">(Figure.5)<\/a> compares how the formula <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-afa19cbce8e213b53250f325166fa39f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#66;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"62\" style=\"vertical-align: 0px;\" \/> is used for rectangular solids and cylinders.<\/p>\n<p>Seeing how a cylinder is similar to a rectangular solid may make it easier to understand the formula for the volume of a cylinder.<\/p>\n<div id=\"CNX_BMath_Figure_09_06_021\" class=\"bc-figure figure\">\n<figure style=\"width: 246px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_021.jpg\" alt=\"In (a), a rectangular solid is shown. The sides are labeled L, W, and H. Below this is V equals capital Bh, then V equals Base times h, then V equals parentheses lw times h, then V equals lwh. In (b), a cylinder is shown. The radius of the top is labeled r, the height is labeled h. Below this is V equals capital Bh, then V equals Base times h, then V equals parentheses pi r squared times h, then V equals pi times r squared times h.\" width=\"246\" height=\"286\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure.5<\/figcaption><\/figure>\n<p id=\"fs-id1171505927833\">To understand the formula for the <span class=\"no-emphasis\" data-type=\"term\">surface area<\/span> of a cylinder, think of a can of vegetables. It has three surfaces: the top, the bottom, and the piece that forms the sides of the can. If you carefully cut the label off the side of the can and unroll it, you will see that it is a rectangle. See <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_06_022\">(Figure.6)<\/a>.<\/p>\n<div id=\"CNX_BMath_Figure_09_06_022\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">By cutting and unrolling the label of a can of vegetables, we can see that the surface of a cylinder is a rectangle. The length of the rectangle is the circumference of the cylinder\u2019s base, and the width is the height of the cylinder.<\/div>\n<figure style=\"width: 431px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_022.jpg\" alt=\"A cylindrical can of green beans is shown. The height is labeled h. Beside this are pictures of circles for the top and bottom of the can and a rectangle for the other portion of the can. Above the circles is C equals 2 times pi times r. The top of the rectangle says l equals 2 times pi times r. The left side of the rectangle is labeled h, the right side is labeled w.\" width=\"431\" height=\"153\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure.6<\/figcaption><\/figure>\n<p id=\"fs-id1876089\">The distance around the edge of the can is the circumference of the cylinder\u2019s base it is also the length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-66a9f474fc3c52efdfb0ba6a70199ee8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#76;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: 0px;\" \/> of the rectangular label. The height of the cylinder is the width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4caed22919a1780df1b6310b338b904e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#87;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"19\" style=\"vertical-align: 0px;\" \/> of the rectangular label. So the area of the label can be represented as<\/p>\n<p><span id=\"fs-id1570430\" data-type=\"media\" data-alt=\"The top line says A equals l times red w. Below the l is 2 times pi times r. Below the w is a red h.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_023_img.jpg\" alt=\"The top line says A equals l times red w. Below the l is 2 times pi times r. Below the w is a red h.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1475242\">To find the total surface area of the cylinder, we add the areas of the two circles to the area of the rectangle.<\/p>\n<p><span id=\"fs-id1551755\" data-type=\"media\" data-alt=\"A rectangle is shown with circles coming off the top and bottom.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_044_img.jpg\" alt=\"A rectangle is shown with circles coming off the top and bottom.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1171498421446\">The surface area of a cylinder with radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> and height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-14b463d0ecd5b350ced6cf1d6a12eef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\" \/>, is<\/p>\n<div id=\"fs-id1171102984009\" class=\"unnumbered\" data-type=\"equation\" data-label=\"\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7238ac6acdb23124ab4cff2dc10d4313_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#50;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#92;&#112;&#105;&#32;&#114;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"131\" style=\"vertical-align: -2px;\" \/><\/div>\n<div data-type=\"equation\" data-label=\"\">\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Volume and Surface Area of a Cylinder<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1650370\">For a cylinder with radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> and height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-14a0eac597f08847f47561f4f8267056_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;&#58;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"19\" style=\"vertical-align: 0px;\" \/><\/p>\n<p><span id=\"fs-id1869917\" data-type=\"media\" data-alt=\"A cylinder is shown. The height is labeled h and the radius of the top is labeled r. Beside it is Volume: V equals pi times r squared times h or V equals capital B times h. Below this is Surface Area: S equals 2 times pi times r squared plus 2 times pi times r times h.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_024.jpg\" alt=\"A cylinder is shown. The height is labeled h and the radius of the top is labeled r. Beside it is Volume: V equals pi times r squared times h or V equals capital B times h. Below this is Surface Area: S equals 2 times pi times r squared plus 2 times pi times r times h.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1768322\" data-type=\"note\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 7<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1474985\" data-type=\"problem\">\n<p id=\"fs-id1553388\">A cylinder has height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> centimetres and radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> centimetres. Find the a) volume and b) surface area.<\/p>\n<\/div>\n<div id=\"fs-id1171488254612\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"fs-id1168466110662\" class=\"unnumbered unstyled\" summary=\"The text reads, \u201cStep 1. Read the problem.\u201d Beside this is an image of a cylinder. The radius is labeled 3, the height is labeled 5.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label<br \/>\nit with the given information.<\/td>\n<td><span id=\"eip-id1168468466750\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_046_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168469800646\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the cylinder<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute. (Use 3.14 for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6fbb54462c586489a95a647feab64a0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"75\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-57d8b381baa86dad1889ee29e6d59707_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#51;&#125;&#94;&#123;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"124\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-50e5fb2ffec1a27766d19c4e30bd6906_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#49;&#52;&#49;&#46;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"79\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> We leave it to you to check your calculations.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume is approximately 141.3 cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468464551\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the surface area of the cylinder<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">S<\/em> = surface area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute. (Use 3.14 for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7238ac6acdb23124ab4cff2dc10d4313_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#50;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#92;&#112;&#105;&#32;&#114;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"131\" style=\"vertical-align: -2px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c88d60b805dbe12cde9231373183c352_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#51;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"228\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c1d581267e28535013cea986db7ac0ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#49;&#53;&#48;&#46;&#55;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"85\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> We leave it to you to check your calculations.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The surface area is approximately 150.72 square inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1562839\" data-type=\"problem\">\n<p id=\"fs-id1587965\">Find the a) volume and b) surface area of the cylinder with radius 4 cm and height 7cm.<\/p>\n<\/div>\n<div id=\"fs-id1581886\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168468741344\" class=\"circled\" type=\"a\">\n<li>351.68 cu. cm<\/li>\n<li>276.32 sq. cm<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1594311\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1334808\" data-type=\"exercise\">\n<div id=\"fs-id1581886\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 7.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1704558\" data-type=\"problem\">\n<p id=\"fs-id1762587\">Find the a) volume and b) surface area of the cylinder with given radius 2 ft and height 8 ft.<\/p>\n<\/div>\n<div id=\"fs-id1330308\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168466030869\" class=\"circled\" type=\"a\">\n<li>100.48 cu. ft<\/li>\n<li>125.6 sq. ft<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171487511722\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1590474\" data-type=\"exercise\">\n<div id=\"fs-id1330308\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 8<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id2143886\" data-type=\"problem\">\n<p id=\"fs-id1171506152146\">Find the a) volume and b) surface area of a can of soda. The radius of the base is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/> centimetres and the height is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-837d0d6b05c238eddf106b68ec9dcfd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> centimetres. Assume the can is shaped exactly like a cylinder.<\/p>\n<\/div>\n<div id=\"fs-id2103175\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168468414539\" class=\"unnumbered unstyled\" summary=\"The text reads, \u201cStep 1. Read the problem.\u201d Beside this is an image of a cylinder. The radius is labeled 4, the height is labeled 13.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and<br \/>\nlabel it with the given information.<\/td>\n<td><span id=\"eip-id1168468414563\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_047_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168468670924\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>a)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the cylinder<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute. (Use 3.14 for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6fbb54462c586489a95a647feab64a0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"75\" style=\"vertical-align: 0px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-be3ae8482f8dae556cbde468e94345f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#52;&#125;&#94;&#123;&#50;&#125;&#92;&#99;&#100;&#111;&#116;&#32;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"134\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8f8cd04d73716f5b2513f8d47161fd46_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#54;&#53;&#51;&#46;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"87\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> We leave it to you to check.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume is approximately 653.12 cubic centimetres.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table id=\"eip-id1168467199006\" class=\"unnumbered unstyled\" summary=\".\" data-label=\"\">\n<tbody>\n<tr>\n<td>b)<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the surface area of the cylinder<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">S<\/em> = surface area<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute. (Use 3.14 for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7238ac6acdb23124ab4cff2dc10d4313_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#50;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#92;&#112;&#105;&#32;&#114;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"131\" style=\"vertical-align: -2px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-81c8a354ef46397a1912eff79d6dfce8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#123;&#52;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#92;&#108;&#101;&#102;&#116;&#40;&#51;&#46;&#49;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#92;&#108;&#101;&#102;&#116;&#40;&#52;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"238\" style=\"vertical-align: -4px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-971931088f7f941d609ae392fafc9122_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#52;&#50;&#55;&#46;&#48;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"86\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> We leave it to you to check your calculations.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The surface area is approximately 427.04 square centimetres.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171505228788\" data-type=\"problem\">\n<p id=\"fs-id1171505228790\">Find the a) volume and b) surface area of a can of paint with radius 8 centimetres and height 19 centimetres. Assume the can is shaped exactly like a cylinder.<\/p>\n<\/div>\n<div id=\"fs-id1792934\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168466094517\" class=\"circled\" type=\"a\">\n<li>3,818.24 cu. cm<\/li>\n<li>1,356.48 sq. cm<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1426872\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1171505275146\" data-type=\"exercise\">\n<div id=\"fs-id1792934\" data-type=\"solution\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 8.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1555240\" data-type=\"problem\">\n<p id=\"fs-id1612789\">Find the a) volume and b) surface area of a cylindrical drum with radius 2.7 feet and height 4 feet. Assume the drum is shaped exactly like a cylinder.<\/p>\n<\/div>\n<div id=\"fs-id1594954\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<ol id=\"eip-id1168467310156\" class=\"circled\" type=\"a\">\n<li>91.5624 cu. ft<\/li>\n<li>113.6052 sq. ft<\/li>\n<\/ol>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h1>Find the Volume of Cones<\/h1>\n<p id=\"fs-id1171505792760\">The first image that many of us have when we hear the word \u2018cone\u2019 is an ice cream cone. There are many other applications of cones (but most are not as tasty as ice cream cones). In this section, we will see how to find the volume of a cone.<\/p>\n<p id=\"fs-id1673945\">In geometry, a cone is a solid figure with one circular base and a vertex. The height of a cone is the distance between its base and the vertex.The cones that we will look at in this section will always have the height perpendicular to the base. See <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_06_029\">(Figure.6)<\/a>.<\/p>\n<div id=\"CNX_BMath_Figure_09_06_029\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">The height of a cone is the distance between its base and the vertex.<\/div>\n<figure style=\"width: 136px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_029.jpg\" alt=\"An image of a cone is shown. The top is labeled vertex. The height is labeled h. The radius of the base is labeled r.\" width=\"136\" height=\"132\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure.6<\/figcaption><\/figure>\n<p id=\"fs-id1171505778220\">Earlier in this section, we saw that the volume of a cylinder is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ab3997f8c104d5269f58ccc93a6a6c4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#92;&#112;&#105;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"75\" style=\"vertical-align: 0px;\" \/>. We can think of a cone as part of a cylinder. <a class=\"autogenerated-content\" href=\"#CNX_BMath_Figure_09_06_030\">Figure.7 <\/a>shows a cone placed inside a cylinder with the same height and same base. If we compare the volume of the cone and the cylinder, we can see that the volume of the cone is less than that of the cylinder.<\/p>\n<div id=\"CNX_BMath_Figure_09_06_030\" class=\"bc-figure figure\">\n<div class=\"bc-figcaption figcaption\">The volume of a cone is less than the volume of a cylinder with the same base and height.<\/div>\n<figure style=\"width: 104px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_030.jpg\" alt=\"An image of a cone is shown. There is a cylinder drawn around it.\" width=\"104\" height=\"138\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\">Figure.7<\/figcaption><\/figure>\n<p id=\"fs-id1550720\">In fact, the volume of a cone is exactly one-third of the volume of a cylinder with the same base and height. The volume of a cone is<\/p>\n<p><span id=\"fs-id993657\" data-type=\"media\" data-alt=\"The formula V equals one-third times capital B times h is shown.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_031_img.jpg\" alt=\"The formula V equals one-third times capital B times h is shown.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1171505277171\">Since the base of a cone is a circle, we can substitute the formula of area of a circle, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4418372e957b5b3eef92a14e3a13b1c1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;&#123;&#114;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"26\" style=\"vertical-align: 0px;\" \/> , for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-770fd1447ccf2fc229801b486b0d8f8a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#66;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"14\" style=\"vertical-align: 0px;\" \/> <em data-effect=\"italics\">to get the formula for volume of a cone.<\/em><\/p>\n<p><span id=\"fs-id2091497\" data-type=\"media\" data-alt=\"The formula V equals one-third times pi times r squared times h is shown.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_032_img.jpg\" alt=\"The formula V equals one-third times pi times r squared times h is shown.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-id1171488303412\">In this book, we will only find the volume of a cone, and not its surface area.<\/p>\n<div class=\"textbox textbox--key-takeaways\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Volume of a Cone<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1171499420872\">For a cone with radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> and height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-14b463d0ecd5b350ced6cf1d6a12eef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\" \/>.<\/p>\n<p><span id=\"fs-id1171496323100\" data-type=\"media\" data-alt=\"An image of a cone is shown. The height is labeled h, the radius of the base is labeled r. Beside this is Volume: V equals one-third times pi times r squared times h.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_033_img.jpg\" alt=\"An image of a cone is shown. The height is labeled h, the radius of the base is labeled r. Beside this is Volume: V equals one-third times pi times r squared times h.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<\/div>\n<div id=\"fs-id1171487154931\" data-type=\"note\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 9<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1598937\" data-type=\"problem\">\n<p id=\"fs-id1598939\">Find the volume of a cone with height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches and radius of its base <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> inches.<\/p>\n<\/div>\n<div id=\"fs-id1171505278364\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168467046430\" class=\"unnumbered unstyled\" summary=\"The text reads, \u201cStep 1. Read the problem.\u201d Beside this is an image of a cone. The radius is labeled 2, the height is labeled 6.\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it<br \/>\nwith the given information.<\/td>\n<td><span id=\"eip-id1168469795158\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_048_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the cone<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong><br \/>\nWrite the appropriate formula.<br \/>\nSubstitute. (Use 3.14 for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-725fdfce4cfad707829ebca3f161b455_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#105;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#57;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#46;&#55;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"167\" style=\"vertical-align: -6px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c286506d253a1ff6d74c4875e6d9116c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#55;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#46;&#49;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#54;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"183\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a8faef4d5b4d1d1cb65cb7ec408382eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#50;&#53;&#46;&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"78\" style=\"vertical-align: -1px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> We leave it to you to check your<br \/>\ncalculations.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume is approximately 25.12 cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171513623105\" data-type=\"problem\">\n<p id=\"fs-id1171513623107\">Find the volume of a cone with height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches and radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches<\/p>\n<\/div>\n<div id=\"fs-id1935596\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1935598\">65.94 cu. in.<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1871880\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1476226\" data-type=\"exercise\">\n<div id=\"fs-id1171513623105\" data-type=\"problem\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 9.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1798404\" data-type=\"problem\">\n<p id=\"fs-id1171496945980\">Find the volume of a cone with height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> centimetres and radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> centimetres<\/p>\n<\/div>\n<div id=\"fs-id1870007\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1573574\">235.5 cu. cm<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1759941\" class=\"try\" data-type=\"note\">\n<div id=\"fs-id1798402\" data-type=\"exercise\">\n<div id=\"fs-id1870007\" data-type=\"solution\">\n<div class=\"textbox textbox--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">EXAMPLE 10<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171505276418\" data-type=\"problem\">\n<p id=\"fs-id1759065\">Marty\u2019s favorite gastro pub serves french fries in a paper wrap shaped like a cone. What is the volume of a conic wrap that is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches tall and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> inches in diametre? Round the answer to the nearest hundredth.<\/p>\n<\/div>\n<div id=\"fs-id1571241\" data-type=\"solution\">\n<div data-type=\"title\"><\/div>\n<div data-type=\"title\"><strong>Solution<\/strong><\/div>\n<table id=\"eip-id1168469874277\" class=\"unnumbered unstyled\" summary=\"Step 1 says, \u201cRead the problem. Draw the figure and label it with the given information. Notice here that the base is the circle at the top of the cone.\u201d The word \u201cread\u201d is in bold. Beside this is an image of a cone. The diametre of the circle at the top of the cone is labeled 5. The height of the cone is labeled 8. Step 2 says, \u201cIdentify what you are looking for.\u201d The word \u201cidentify\u201d is in bold. Beside this it says, \u201cthe volume of the cone.\u201d Step 3 says, \u201cName. Choose a variable to represent it.\u201d The word \u201cname\u201d is in bold. Beside this it says, \u201clet V equal volume.\u201d Step 4 says, \u201cTranslate. Write the appropriate formula. Substitute. (Use 3.14 for pi, and notice that we were given the distance across the circle, which is its diametre. The radius is 2.5 inches.)\u201d The word \u201ctranslate\u201d is in bold. Beside this is V equals one-third times pi times r squared times h. Below that is V is approximately one-third times 3.14 times 2.5 in. squared times 8 in. Step 5 says, \u201cSolve the equation.\u201d The word \u201csolve\u201d is in bold. Beside this is V is approximately 52.33. Step 6 says, \u201cCheck,\u201d in bold. Then \u201cWe leave it to you to check your arithmetic.\u201d Step 7 says, \u201cAnswer the question.\u201d The word \u201canswer\u201d is in bold. The answer is given as \u201cThe volume of the wrap is approximately 52.33 cubic inches.\u201d\" data-label=\"\">\n<tbody>\n<tr>\n<td>Step 1. <strong data-effect=\"bold\">Read<\/strong> the problem. Draw the figure and label it with the given information. Notice here that the base is the circle at the top of the cone.<\/td>\n<td><span id=\"eip-id1168466154518\" data-type=\"media\" data-alt=\".\"><img decoding=\"async\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_049_img-01.png\" alt=\".\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<\/tr>\n<tr>\n<td>Step 2. <strong data-effect=\"bold\">Identify<\/strong> what you are looking for.<\/td>\n<td>the volume of the cone<\/td>\n<\/tr>\n<tr>\n<td>Step 3. <strong data-effect=\"bold\">Name.<\/strong> Choose a variable to represent it.<\/td>\n<td>let <em data-effect=\"italics\">V<\/em> = volume<\/td>\n<\/tr>\n<tr>\n<td>Step 4. <strong data-effect=\"bold\">Translate.<\/strong> Write the appropriate formula. Substitute. (Use 3.14 for <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-26d6788550ffd50fe94542bb3e8ee615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#92;&#112;&#105;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\" \/>, and notice that we were given the distance across the circle, which is its diametre. The radius is 2.5 inches.)<\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a78a22a56df5f35d86016f6d8537ff82_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#112;&#105;&#32;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#46;&#51;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#50;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"180\" style=\"vertical-align: -6px;\" \/><br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d5cdc10c0d3bda0a66495827d249e7d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#48;&#46;&#55;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#51;&#46;&#49;&#52;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#123;&#92;&#108;&#101;&#102;&#116;&#40;&#50;&#46;&#53;&#92;&#114;&#105;&#103;&#104;&#116;&#41;&#125;&#94;&#123;&#50;&#125;&#92;&#112;&#104;&#97;&#110;&#116;&#111;&#109;&#123;&#92;&#114;&#117;&#108;&#101;&#123;&#49;&#101;&#109;&#125;&#123;&#48;&#101;&#120;&#125;&#125;&#92;&#108;&#101;&#102;&#116;&#40;&#56;&#92;&#114;&#105;&#103;&#104;&#116;&#41;\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"197\" style=\"vertical-align: -6px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 5. <strong data-effect=\"bold\">Solve.<\/strong><\/td>\n<td><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b4de6b414d8b6c23b4e72f052033da6e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#92;&#97;&#112;&#112;&#114;&#111;&#120;&#32;&#53;&#50;&#46;&#51;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"79\" style=\"vertical-align: 0px;\" \/><\/td>\n<\/tr>\n<tr>\n<td>Step 6. <strong data-effect=\"bold\">Check:<\/strong> We leave it to you to check your calculations.<\/td>\n<td><\/td>\n<\/tr>\n<tr>\n<td>Step 7. <strong data-effect=\"bold\">Answer<\/strong> the question.<\/td>\n<td>The volume of the wrap is approximately 52.33 cubic inches.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.1<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1171497994886\" data-type=\"problem\">\n<p id=\"fs-id1171497994888\">How many cubic inches of candy will fit in a cone-shaped pi\u00f1ata that is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0272b752bb5d0877335745c22f2f27ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> inches long and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-40f7428479801bf4ef27a5149e9df526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> inches across its base? Round the answer to the nearest hundredth.<\/p>\n<\/div>\n<div id=\"fs-id1592722\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1592725\">678.24 cu. in.<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">TRY IT 10.2<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<div id=\"fs-id1903325\" data-type=\"problem\">\n<p id=\"fs-id1399880\">What is the volume of a cone-shaped party hat that is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> inches tall and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches across at the base? Round the answer to the nearest hundredth.<\/p>\n<\/div>\n<div id=\"fs-id1787346\" data-type=\"solution\">\n<details open=\"open\">\n<summary>Show answer<\/summary>\n<p id=\"fs-id1787349\">128.2 cu. in.<\/p>\n<\/details>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-id1171505925375\" class=\"media-2\" data-type=\"note\">\n<div data-type=\"title\">ACCESS ADDITIONAL ONLINE RESOURCES<\/div>\n<ul id=\"fs-id1171498402192\">\n<li><a href=\"http:\/\/openstaxcollege.org\/l\/24volcone\">Volume of a Cone<\/a><\/li>\n<\/ul>\n<h1 data-type=\"title\">Key Concepts<\/h1>\n<ul id=\"eip-100\">\n<li><strong>Volume and Surface Area of a Rectangular Solid<\/strong>\n<ul id=\"eip-id3755293\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-70441d53f3f0f6969e5be735ccb8b3f2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#76;&#87;&#72;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"85\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-87093e0b1202288d622c31bdb6c49782_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#50;&#76;&#72;&#43;&#50;&#76;&#87;&#43;&#50;&#87;&#72;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"200\" style=\"vertical-align: -2px;\" \/><\/li>\n<\/ul>\n<\/li>\n<li><strong>Volume and Surface Area of a Cube<\/strong>\n<ul id=\"eip-id1171779023695\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-edc9b90cd61abac690fd07c160d33677_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#123;&#115;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"53\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-3e7cdf899a512101dcb9bdc85022f87c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#54;&#123;&#115;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"60\" style=\"vertical-align: 0px;\" \/><\/li>\n<\/ul>\n<\/li>\n<li><strong>Volume and Surface Area of a Sphere<\/strong>\n<ul id=\"eip-id1171783978818\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7c7e25a744b15835f98879ff2be16df7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#52;&#125;&#123;&#51;&#125;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#51;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"75\" style=\"vertical-align: -6px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-cef1f49eebfcd3582a52a057f75f77a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#52;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"71\" style=\"vertical-align: -1px;\" \/><\/li>\n<\/ul>\n<\/li>\n<li><strong>Volume and Surface Area of a Cylinder<\/strong>\n<ul id=\"eip-id1171793481149\">\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6fbb54462c586489a95a647feab64a0a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"75\" style=\"vertical-align: 0px;\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-7238ac6acdb23124ab4cff2dc10d4313_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#83;&#61;&#50;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#43;&#50;&#92;&#112;&#105;&#32;&#114;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"131\" style=\"vertical-align: -2px;\" \/><\/li>\n<\/ul>\n<\/li>\n<li><strong>Volume of a Cone<\/strong>\n<ul id=\"eip-id1171782886821\">\n<li>For a cone with radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#114;\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\" \/> and height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-14b463d0ecd5b350ced6cf1d6a12eef3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"10\" style=\"vertical-align: 0px;\" \/>:<br \/>\nVolume: <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-d667667489cc5c52babfc35a69f51ee1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#86;&#61;&#92;&#102;&#114;&#97;&#99;&#123;&#49;&#125;&#123;&#51;&#125;&#92;&#112;&#105;&#32;&#123;&#114;&#125;&#94;&#123;&#50;&#125;&#104;\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"86\" style=\"vertical-align: -6px;\" \/><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<h1>Glossary<\/h1>\n<div class=\"textbox shaded\">\n<dl id=\"fs-id2063975\">\n<dt>cone<\/dt>\n<dd id=\"fs-id1171505120588\">A cone is a solid figure with one circular base and a vertex.<\/dd>\n<\/dl>\n<dl id=\"fs-id2036687\">\n<dt>cube<\/dt>\n<dd id=\"fs-id1417511\">A cube is a rectangular solid whose length, width, and height are equal.<\/dd>\n<\/dl>\n<dl id=\"fs-id1417515\">\n<dt>cylinder<\/dt>\n<dd id=\"fs-id1171487155088\">A cylinder is a solid figure with two parallel circles of the same size at the top and bottom.<\/dd>\n<\/dl>\n<\/div>\n<h1 data-type=\"title\">Practice Makes Perfect<\/h1>\n<h2 id=\"fs-id1614121\">Find Volume and Surface Area of Rectangular Solids<\/h2>\n<p>In the following exercises, find a) the volume and b) the surface area of the rectangular solid with the given dimensions.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">1. length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> metres, width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2b2514947ef7a7471f9fcd9c60117cf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"21\" style=\"vertical-align: -1px;\" \/> metres, height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> metres<\/td>\n<td style=\"width: 50%;\">2. length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> feet, width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet, height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-01948ea56b434f27f412043e785fe880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> feet<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">3. length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a880aa3dee267fff1a375dd7cfcaa389_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> yards, width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-66970d52d08b82792213391aabdbe414_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/> yards, height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e6525f8fad84f7bac48f1160b565c854_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"23\" style=\"vertical-align: -1px;\" \/> yards<\/td>\n<td style=\"width: 50%;\">4. length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2f26ee8cbd5420ef3ba29eea50398f4d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#46;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\" \/> centimetres, width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-884260fd9f998afa1aa3b70c9fe6b61f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> centimetres, height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b51aa9707a66a85997f31501edc50c65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/> centimetres<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1797305\">In the following exercises, solve.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">5.<strong data-effect=\"bold\"> Moving van<\/strong> A rectangular moving van has length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8dde8d4cade60a4f3ca0e779512b974c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> feet, width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet, and height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet. Find its a) volume and b) surface area.<\/td>\n<td style=\"width: 50%;\">6. <strong data-effect=\"bold\">Gift box<\/strong> A rectangular gift box has length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-fc1c5ee273f78a117868c9594082c74b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> inches, width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8dde8d4cade60a4f3ca0e779512b974c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> inches, and height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/> inches. Find its a) volume and b) surface area.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">7.<strong data-effect=\"bold\"> Carton<\/strong> A rectangular carton has length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2c4479ffb743fdcac539db9dd148e1c6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#49;&#46;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"32\" style=\"vertical-align: -1px;\" \/> cm, width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1fc1f662d642114a283afc56742cedb5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> cm, and height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-884260fd9f998afa1aa3b70c9fe6b61f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> cm. Find its a) volume and b) surface area.<\/td>\n<td style=\"width: 50%;\">8.<strong>Shipping container<\/strong> A rectangular shipping container has length <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-67c7495a45a67e3bca7cf3ac459bc898_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#50;&#46;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"32\" style=\"vertical-align: 0px;\" \/> feet, width <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-18a69ce801ebb07a7893aeb4b5b8b4d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> feet, and height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-17f9334def3aeb2025134bd752d0dea3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"22\" style=\"vertical-align: 0px;\" \/> feet. Find its a) volume and b) surface area.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1171505779653\">In the following exercises, find a) the volume and b) the surface area of the cube with the given side length.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">9. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> centimetres<\/td>\n<td style=\"width: 50%;\">10. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">11. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-110ffb20e30a4c62dda047c98653a72c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> feet<\/td>\n<td style=\"width: 50%;\">12. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0154243e4669a75b5cdfd1ed3f8759ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"30\" style=\"vertical-align: -1px;\" \/> metres<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id2238334\">In the following exercises, solve.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">13. <strong data-effect=\"bold\">Science center<\/strong> Each side of the cube at the Discovery Science Center in Santa Ana is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-de25eb06760758d2c59eb63fca270413_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> feet long. Find its a) volume and b) surface area.<\/td>\n<td style=\"width: 50%;\">14. <strong data-effect=\"bold\">Museum<\/strong> A cube-shaped museum has sides <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1a494309aca1bdc45eb593f8e8497226_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"17\" style=\"vertical-align: -1px;\" \/> metres long. Find its a) volume and b) surface area.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">15. <strong data-effect=\"bold\">Base of statue<\/strong> The base of a statue is a cube with sides <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec778b275453b1720f4962450010c189_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\" \/> metres long. Find its a) volume and b) surface area.<\/td>\n<td style=\"width: 50%;\">16.<strong data-effect=\"bold\"> Tissue box<\/strong> A box of tissues is a cube with sides 4.5 inches long. Find its a) volume and b) surface area.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1171487568616\"><strong data-effect=\"bold\"><br \/>\n<\/strong>Find the Volume and Surface Area of Spheres<\/h2>\n<p id=\"eip-236\">In the following exercises, find a) the volume and b) the surface area of the sphere with the given radius. Round answers to the nearest hundredth.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">17. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> centimetres<\/td>\n<td style=\"width: 50%;\">18. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">19. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-0f1744ffd0a5d1d7e31cd59aefe01c6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> feet<\/td>\n<td style=\"width: 50%;\">20. <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-66970d52d08b82792213391aabdbe414_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/> yards<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1171498398848\">In the following exercises, solve. Round answers to the nearest hundredth.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">21.<strong data-effect=\"bold\"> Exercise ball<\/strong> An exercise ball has a radius of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b59223d2c162a0fdd163af8597f0845e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -1px;\" \/> inches. Find its a) volume and b) surface area.<\/td>\n<td style=\"width: 50%;\">22. <strong data-effect=\"bold\">Balloon ride<\/strong> The Great Park Balloon is a big orange sphere with a radius of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-dce5a8d8a80b6aa9c2a9f6810851e582_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> feet . Find its a) volume and b) surface area.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">23. <strong data-effect=\"bold\">Golf ball<\/strong> A golf ball has a radius of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8fac357af10206befdb463e651007c5d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"22\" style=\"vertical-align: -1px;\" \/> centimetres. Find its a) volume and b) surface area.<\/td>\n<td style=\"width: 50%;\">24.<strong data-effect=\"bold\"> Baseball<\/strong> A baseball has a radius of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a2012329e6d3ba6f279df2b9d225abe4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\" \/> inches. Find its a) volume and b) surface area.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1999562\"><strong data-effect=\"bold\"><br \/>\n<\/strong>Find the Volume and Surface Area of a Cylinder<\/h2>\n<p id=\"eip-233\">In the following exercises, find a) the volume and b) the surface area of the cylinder with the given radius and height. Round answers to the nearest hundredth.<\/p>\n<table style=\"border-collapse: collapse; width: 100%; height: 56px;\">\n<tbody>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">25. radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet, height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet<\/td>\n<td style=\"width: 50%; height: 14px;\">26. radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> centimetres, height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b59223d2c162a0fdd163af8597f0845e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"16\" style=\"vertical-align: -1px;\" \/> centimetres<\/td>\n<\/tr>\n<tr style=\"height: 14px;\">\n<td style=\"width: 50%; height: 14px;\">27. radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-2b2514947ef7a7471f9fcd9c60117cf9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"21\" style=\"vertical-align: -1px;\" \/> metres, height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b51aa9707a66a85997f31501edc50c65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/> metres<\/td>\n<td style=\"width: 50%; height: 14px;\">28. radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-f3444057b4da40f5d1286ea53e4b8390_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#46;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: -1px;\" \/> yards, height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-ec778b275453b1720f4962450010c189_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"23\" style=\"vertical-align: 0px;\" \/> yards<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1171506675298\">In the following exercises, solve. Round answers to the nearest hundredth.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">29.<strong data-effect=\"bold\"> Coffee can<\/strong> A can of coffee has a radius of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> cm and a height of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-837d0d6b05c238eddf106b68ec9dcfd6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> cm. Find its a) volume and b) surface area.<\/td>\n<td style=\"width: 50%;\">30.<strong data-effect=\"bold\"> Snack pack<\/strong> A snack pack of cookies is shaped like a cylinder with radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/> cm and height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4a1d3ea4963f568cabd97329456036b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> cm. Find its a) volume and b) surface area.<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">31.<strong data-effect=\"bold\"> Barber shop pole<\/strong> A cylindrical barber shop pole has a diametre of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches and height of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-762747d84dc941b4e4b85f0d3d4eb09e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: -1px;\" \/> inches. Find its a) volume and b) surface area.<\/td>\n<td style=\"width: 50%;\">32. <strong data-effect=\"bold\">Architecture<\/strong> A cylindrical column has a diametre of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet and a height of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-80588c2af70b499bde2614a130c98b76_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> feet. Find its a) volume and b) surface area.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 id=\"fs-id1171505779470\"><strong data-effect=\"bold\"><br \/>\n<\/strong>Find the Volume of Cones<\/h2>\n<p>In the following exercises, find the volume of the cone with the given dimensions. Round answers to the nearest hundredth.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">33. height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e99b7c7ddd421682faf67e5b5f865882_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#57;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet and radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-e584dd0bab4e6c8efc164939c28db757_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\" \/> feet<\/td>\n<td style=\"width: 50%;\">34. height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches and radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">35. height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5ce7bdea5a486ad088876ca8457fff6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;&#46;&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: -1px;\" \/> centimetres and radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-8995e2084120c1c1f4b53f490d281bc4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"8\" style=\"vertical-align: 0px;\" \/> cm<\/td>\n<td style=\"width: 50%;\">36. height <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-1b6e389d07179c8315c2bb62b4456ffe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#53;&#46;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"30\" style=\"vertical-align: -1px;\" \/> metres and radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-6111a899fd636b7a5238708f8679f6ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#52;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: -1px;\" \/> metres<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p id=\"fs-id1563637\">In the following exercises, solve. Round answers to the nearest hundredth.<\/p>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">37.<strong data-effect=\"bold\"> Teepee<\/strong> What is the volume of a cone-shaped teepee tent that is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> feet tall and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> feet across at the base?<\/td>\n<td style=\"width: 50%;\">38. <strong data-effect=\"bold\">Popcorn cup<\/strong> What is the volume of a cone-shaped popcorn cup that is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches tall and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b5c3e12330dabaeec7413281aba0f134_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#54;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches across at the base?<\/td>\n<\/tr>\n<tr>\n<td style=\"width: 50%;\">39. <strong data-effect=\"bold\">Silo<\/strong> What is the volume of a cone-shaped silo that is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-39e5271c62d377c7a347b4eb07f74ab2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#53;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> feet tall and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-87249b4c68e9c45ed2c73045ffb24b4b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"18\" style=\"vertical-align: 0px;\" \/> feet across at the base?<\/td>\n<td style=\"width: 50%;\">40. <strong data-effect=\"bold\">Sand pile<\/strong> What is the volume of a cone-shaped pile of sand that is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-40f7428479801bf4ef27a5149e9df526_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#50;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"16\" style=\"vertical-align: -1px;\" \/> metres tall and <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-874b63beceda768488ea76f12b9cf9e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> metres across at the base?<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 style=\"text-align: left;\" data-type=\"title\">Everyday Math<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1171506170826\">41.<strong data-effect=\"bold\"> Street light post<\/strong> The post of a street light is shaped like a truncated cone, as shown in the picture below. It is a large cone minus a smaller top cone. The large cone is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-874b63beceda768488ea76f12b9cf9e9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: 0px;\" \/> feet tall with base radius <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-4868771cbc422b5818f85500909ce433_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"7\" style=\"vertical-align: -1px;\" \/> foot. The smaller cone is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-5450913cc453faf132dc56e5965ca797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#49;&#48;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"17\" style=\"vertical-align: -1px;\" \/> feet tall with base radius of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-b7ab7f7da74090c2370accce55f96e3b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#48;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> feet. To the nearest tenth,<\/p>\n<p id=\"fs-id1591208\">a) find the volume of the large cone.<\/p>\n<p id=\"fs-id1591211\">b) find the volume of the small cone.<\/p>\n<p id=\"fs-id1171505984458\">c) find the volume of the post by subtracting the volume of the small cone from the volume of the large cone.<\/p>\n<p><span id=\"fs-id1691040\" data-type=\"media\" data-alt=\"An image of a cone is shown. There is a dark dotted line at the top indicating a smaller cone.\"><img decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/opentextbc.ca\/accessibilitytoolkit\/wp-content\/uploads\/sites\/333\/2021\/03\/CNX_BMath_Figure_09_06_201_img.jpg\" alt=\"An image of a cone is shown. There is a dark dotted line at the top indicating a smaller cone.\" data-media-type=\"image\/jpeg\" \/><\/span><\/td>\n<td style=\"width: 50%;\">\n<p id=\"fs-id1574935\">42. <strong data-effect=\"bold\">Ice cream cones<\/strong> A regular ice cream cone is 4 inches tall and has a diametre of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-01948ea56b434f27f412043e785fe880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#50;&#46;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"22\" style=\"vertical-align: 0px;\" \/> inches. A waffle cone is <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-aca3387e59afe477960eabc2f23b3db5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#55;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"9\" style=\"vertical-align: 0px;\" \/> inches tall and has a diametre of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-a005928d9ea75d0170b694f5cffc8c65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#51;&#46;&#50;&#53;\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"31\" style=\"vertical-align: 0px;\" \/> inches. To the nearest hundredth,<\/p>\n<p id=\"fs-id1171498001417\">a) find the volume of the regular ice cream cone.<\/p>\n<p id=\"fs-id1758963\">b) find the volume of the waffle cone.<\/p>\n<p id=\"fs-id1758966\">c) how much more ice cream fits in the waffle cone compared to the regular cone?<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2 style=\"text-align: left;\" data-type=\"title\">Writing Exercises<\/h2>\n<table style=\"border-collapse: collapse; width: 100%;\">\n<tbody>\n<tr>\n<td style=\"width: 50%;\">43. The formulas for the volume of a cylinder and a cone are similar. Explain how you can remember which formula goes with which shape.<\/td>\n<td style=\"width: 50%;\">44. Which has a larger volume, a cube of sides of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet or a sphere with a diametre of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/opentextbc.ca\/introalgebra\/wp-content\/ql-cache\/quicklatex.com-23212a120eb92d226d44696a0b80bead_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"&#56;\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\" \/> feet? Explain your reasoning.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1 style=\"text-align: left;\">Answers<\/h1>\n<table style=\"border-collapse: collapse; width: 100%; height: 595px;\">\n<tbody>\n<tr style=\"height: 103px;\">\n<td style=\"width: 33.3333%; height: 103px;\">1.<\/p>\n<p>a) 9 cu. m<\/p>\n<p>b) 27 sq. m<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">3.<\/p>\n<p>a) 17.64 cu. yd.<\/p>\n<p>b) 41.58 sq. yd.<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">5.<\/p>\n<p>a) 1,024 cu. ft<\/p>\n<p>b) 640 sq. ft<\/td>\n<\/tr>\n<tr style=\"height: 103px;\">\n<td style=\"width: 33.3333%; height: 103px;\">7.<\/p>\n<div id=\"fs-id1171497077335\" data-type=\"exercise\">\n<div id=\"fs-id1171506678898\" data-type=\"solution\">\n<p>a) 3,350.49 cu. cm<\/p>\n<p>b) 1,622.42 sq. cm<\/p>\n<\/div>\n<\/div>\n<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">9.<\/p>\n<p>a) 125 cu. cm<\/p>\n<p>b) 150 sq. cm<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">11.<\/p>\n<p>a) 1124.864 cu. ft.<\/p>\n<p>b) 648.96 sq. ft<\/td>\n<\/tr>\n<tr style=\"height: 103px;\">\n<td style=\"width: 33.3333%; height: 103px;\">13.<\/p>\n<div id=\"fs-id2238338\" data-type=\"exercise\">\n<div id=\"fs-id1864381\" data-type=\"solution\">\n<p>a) 262,144 cu. ft<\/p>\n<p>b) 24,576 sq. ft<\/p>\n<\/div>\n<\/div>\n<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">15.<\/p>\n<div id=\"fs-id1171513623124\" data-type=\"exercise\">\n<div id=\"fs-id1930588\" data-type=\"solution\">\n<p>a) 21.952 cu. m<\/p>\n<p>b) 47.04 sq. m<\/p>\n<\/div>\n<\/div>\n<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">17.<\/p>\n<p>a) 113.04 cu. cm<\/p>\n<p>b) 113.04 sq. cm<\/td>\n<\/tr>\n<tr style=\"height: 103px;\">\n<td style=\"width: 33.3333%; height: 103px;\">19.<\/p>\n<div id=\"fs-id2024197\" data-type=\"exercise\">\n<div id=\"fs-id1555719\" data-type=\"solution\">\n<p>a) 1,766.25 cu. ft<\/p>\n<p>b) 706.5 sq. ft<\/p>\n<\/div>\n<\/div>\n<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">21.<\/p>\n<p>a) 14,130 cu. in.<\/p>\n<p>b) 2,826 sq. in.<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">23.<\/p>\n<p>a) 381.51 cu. cm<\/p>\n<p>b) 254.34 sq. cm<\/td>\n<\/tr>\n<tr style=\"height: 103px;\">\n<td style=\"width: 33.3333%; height: 103px;\">25.<\/p>\n<p>a) 254.34 cu. ft<\/p>\n<p>b) 226.08 sq. ft<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">27.<\/p>\n<p>a) 29.673 cu. m<\/p>\n<p>b) 53.694 sq. m<\/td>\n<td style=\"width: 33.3333%; height: 103px;\">29.<\/p>\n<p>a) 1,020.5 cu. cm<\/p>\n<p>b) 565.2 sq. cm<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">31.<\/p>\n<p>a) 678.24 cu. in.<\/p>\n<p>b) 508.68 sq. in.<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">33. 37.68 cu. ft<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">35. 324.47 cu. cm<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">37. 261.67 cu. ft<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">39. 64,108.33 cu. ft<\/td>\n<td style=\"width: 33.3333%; height: 16px;\">41.<\/p>\n<p>a) 31.4 cu. ft<\/p>\n<p>b) 2.6 cu. ft<\/p>\n<p>c) 28.8 cu. ft<\/td>\n<\/tr>\n<tr style=\"height: 16px;\">\n<td style=\"width: 33.3333%; height: 16px;\">43.\u00a0Answers will vary.<\/td>\n<td style=\"width: 33.3333%; height: 16px;\"><\/td>\n<td style=\"width: 33.3333%; height: 16px;\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h1>Attributions<\/h1>\n<ul>\n<li>This chapter has been adapted from \u201cSolve Geometry Applications: Volume and Surface Area\u201d in <a href=\"https:\/\/openstax.org\/details\/books\/prealgebra-2e\"><em>Prealgebra<\/em><\/a> (OpenStax) by Lynn Marecek, MaryAnne Anthony-Smith, and Andrea Honeycutt Mathis, which is under a <a href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY 4.0 Licence<\/a>. Adapted by Izabela Mazur. See the Copyright page for more information.<\/li>\n<\/ul>\n","protected":false},"author":90,"menu_order":3,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-557","chapter","type-chapter","status-publish","hentry"],"part":398,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/557","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":1,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/557\/revisions"}],"predecessor-version":[{"id":558,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/557\/revisions\/558"}],"part":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/parts\/398"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapters\/557\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/media?parent=557"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=557"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/contributor?post=557"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/introalgebra\/wp-json\/wp\/v2\/license?post=557"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}