CHAPTER 3 Measurement, Perimeter, Area, and Volume
Systems of Measurement
In the following exercises, convert between Imperial units. Round to the nearest tenth.
|1. A picture frame is inches wide. Convert the width to feet.||2. A floral arbor is feet tall. Convert the height to inches.|
|3. A playground is feet wide. Convert the width to yards.||4. Kelly is feet inches tall. Convert her height to inches.|
|5. An orca whale in the Salish Sea weighs tons. Convert the weight to pounds.||6. The height of Mount Shasta is feet. Convert the height to miles.|
|7. How many tablespoons are in a quart?||8. The play lasted hours. Convert the time to minutes.|
|9. Trinh needs cups of paint for her class art project. Convert the volume to gallons.||10. Naomi’s baby weighed pounds ounces at birth. Convert the weight to ounces.|
In the following exercises, solve, and state your answer in mixed units.
|11. Every day last week, Pedro recorded the amount of time he spent reading. He read for minutes. How much time, in hours and minutes, did Pedro spend reading?||12. John caught lobsters. The weights of the lobsters were pound ounces, pound ounces, pounds ounces, and pounds ounces. What was the total weight of the lobsters?|
|13. Dalila wants to make pillow covers. Each cover takes inches of fabric. How many yards and inches of fabric does she need for pillow covers?||14. Fouad is feet inches tall. If he stands on a rung of a ladder feet inches high, how high off the ground is the top of Fouad’s head?|
In the following exercises, convert between metric units.
|15. Mount Everest is metres tall. Convert the height to kilometres.||16. Donna is metres tall. Convert her height to centimetres.|
|17. One cup of yogurt contains grams of protein. Convert this to milligrams.||18. One cup of yogurt contains milligrams of calcium. Convert this to grams.|
|19. A bottle of water contained millilitre s. Convert this to litres.||20. Sergio weighed kilograms at birth. Convert this to grams.|
In the following exercises, solve.
|21. Selma had a bottle of water. If she drank millilitres, how much water, in millilitres, was left in the bottle?||22. Minh is metres tall. His daughter is centimetres tall. How much taller, in metres, is Minh than his daughter?|
|23. One ounce of tofu provides grams of protein. How many milligrams of protein are provided by ounces of tofu?||24. One serving of cranberry juice contains grams of sugar. How many kilograms of sugar are in servings of cranberry juice?|
In the following exercises, convert between Imperial and metric units. Round to the nearest tenth.
|25. A college basketball court is feet long. Convert this length to metres.||26. Majid is inches tall. Convert his height to centimetres.|
|27. Lucas weighs kilograms. Convert his weight to pounds.||28. Caroline walked kilometres. Convert this length to miles.|
|29. A box of books weighs pounds. Convert this weight to kilograms.||30. Steve’s car holds litres of gas. Convert this to gallons.|
In the following exercises, convert the Fahrenheit temperatures to degrees Celsius. Round to the nearest tenth.
|31. °F||32. °F|
|33. °F||34. °F|
In the following exercises, convert the Celsius temperatures to degrees Fahrenheit. Round to the nearest tenth.
|35. °C||36. °C|
|37. °C||38. °C|
Understand Linear, Square, Cubic Measure
In the following exercises, would you measure each item using linear, square, or cubic measure?
|39. amount of sand in a sandbag||40. height of a tree|
|41. size of a patio||42. length of a highway|
In the following exercises, find a) the perimeter b) the area of each figure
Use Properties of Rectangles
In the following exercises, find the a) perimeter b) area of each rectangle
|45. The length of a rectangle is metres and the width is metres.||46. The length of a rectangle is feet and the width is feet.|
|47. A sidewalk in front of Kathy’s house is in the shape of a rectangle feet wide by feet long.||48. A rectangular room is feet wide by feet long.|
In the following exercises, solve.
|49. Find the length of a rectangle with perimeter of centimetres and width of centimetres.||50. Find the width of a rectangle with perimeter and length .|
|51. The area of a rectangle is square metres. The length is metres. What is the width?||52. The width of a rectangle is centimetres. The area is square centimetres. What is the length?|
|53. The length of a rectangle is centimetres more than the width. The perimeter is centimetres. Find the length and the width.||54. The width of a rectangle is more than twice the length. The perimeter is inches. Find the length and the width.|
Use Properties of Triangles
In the following exercises, solve using the properties of triangles.
|55. Find the area of a triangle with base inches and height inches.||56. Find the area of a triangle with base centimetres and height centimetres.|
|57. A triangular road sign has base inches and height inches. What is its area?||58. If a triangular courtyard has sides feet and feet and the perimeter is feet, how long is the third side?|
|59. A tile in the shape of an isosceles triangle has a base of inches. If the perimeter is inches, find the length of each of the other sides.||60. Find the length of each side of an equilateral triangle with perimeter of yards.|
|61. The perimeter of a triangle is feet. One side of the triangle is feet longer than the shortest side. The third side is feet longer than the shortest side. Find the length of each side.||62. One side of a triangle is three times the smallest side. The third side is feet more than the shortest side. The perimeter is feet. Find the lengths of all three sides.|
Use Properties of Trapezoids
In the following exercises, solve using the properties of trapezoids.
|63. The height of a trapezoid is feet and the bases are and feet. What is the area?||64. The height of a trapezoid is yards and the bases are and yards. What is the area?|
|65. Find the area of the trapezoid with height metres and bases and metres.||66. A flag is shaped like a trapezoid with height centimetres and the bases are and centimetres. What is the area of the flag?|
Use Properties of Circles
In the following exercises, solve using the properties of circles. Round answers to the nearest hundredth.
67. A circular mosaic has radius metres. Find the
b) area of the mosaic
68. A circular fountain has radius feet. Find the
b) area of the fountain
|69. Find the diametre of a circle with circumference inches.||70. Find the radius of a circle with circumference centimetres|
Find the Area of Irregular Figures
In the following exercises, find the area of each shaded region.
Find Volume and Surface Area of Rectangular Solids
In the following exercises, find the a) volume b) surface area of the rectangular solid
|77. A rectangular solid with length centimetres, width centimetres, and height centimetres||78. A cube with sides that are feet long|
|79. A cube of tofu with sides inches||80. A rectangular carton with length inches, width inches, and height inches|
Find Volume and Surface Area of Spheres
In the following exercises, find the a) volume b) surface area of the sphere.
|81. a sphere with radius yards||82. a sphere with radius metres|
|83. a baseball with radius inches||84. a soccer ball with radius centimetres|
Find Volume and Surface Area of Cylinders
In the following exercises, find the a) volume b) surface area of the cylinder
|85. A cylinder with radius yards and height yards||86. A cylinder with diametre inches and height inches|
|87. A juice can with diametre centimetres and height centimetres||88. A cylindrical pylon with diametre feet and height feet|
Find Volume of Cones
In the following exercises, find the volume of the cone.
|89. A cone with height metres and radius metre||90. A cone with height feet and radius feet|
|91. A cone-shaped water cup with diametre inches and height inches||92. A cone-shaped pile of gravel with diametre yards and height yards|
|1. 3.5 feet||3. 15 yards||5. 9000 pounds|
|7. 64 tablespoons||9. 1.9 gallons||11. 7 hours 10 minutes|
|13. 3 yards, 12 inches||15. 8.85 kilometres||17. 13,000 milligrams|
|19. 0.65 litres||21. 855 millilitre s||23. 10,000 milligrams|
|25. 25.6 metres||27. 171.6 pounds||29. 11.4 kilograms|
|31. °C||33. °C||35. °F|
|37. °F||39. cubic||41. square|
a) 8 units
b) 3 sq. units
a) 140 m
b) 1176 sq. m
a) 98 ft.
b) 180 sq. ft.
|49. 25 cm||51. 62 m||53. 24.5 in., 12.5 in.|
|55. 135 sq. in.||57. 600 sq. in.||59. 7 in., 7 in.|
|61. 17 ft., 20 ft., 22 ft.||63. 100 sq. ft.||65. 675 sq. m|
a) 18.84 m
b) 28.26 sq. m
|69. 48 in.||71. 30 sq. units|
|73. 300 sq. units||75. 199.25 sq. units||77.
a) 630 cu. cm
b) 496 sq. cm
a) 15.625 cu. in.
b) 37.5 sq. in.
a) 267.95 cu. yd.
b) 200.96 sq. yd.
a) 12.76 cu. in.
b) 26.41 sq. in.
a) 75.36 cu. yd.
b) 100.48 sq. yd.
a) 753.6 cu. cm
b) 477.28 sq. cm
|89. 5.233 cu. m|
|91. 4.599 cu. in.|
In the following exercises, solve using the appropriate unit conversions.
|1. One cup of milk contains milligrams of calcium. Convert this to grams.||2. Azize walked miles. Convert this distance to feet.|
|3. Janice ran kilometres. Convert this distance to miles. Round to the nearest hundredth of a mile.||4. Larry had phone customer phone calls yesterday. The calls lasted minutes. How much time, in hours and minutes, did Larry spend on the phone?|
|5. Use the formula to convert °C to degrees||6. Yolie is inches tall. Convert her height to centimetres. Round to the nearest centimetre.|
|7. A triangular poster has base centimetres and height centimetres. Find the area of the poster.||8. The length of a rectangle is feet more than five times the width. The perimeter is feet. Find the dimensions of the rectangle.|
|9. A circular pool has diametre inches. What is its circumference? Round to the nearest tenth.||10. A trapezoid has height inches and bases inches and inches. Find the area of the trapezoid.|
|11. Find the volume of a rectangular room with width feet, length feet, and height feet.||
12. Find the area of the shaded region. Round to the nearest tenth.
|13. A traffic cone has height centimetres. The radius of the base is centimetres. Find the volume of the cone. Round to the nearest tenth.||14. A coffee can is shaped like a cylinder with height inches and radius inches. Find (a) the surface area and (b) the volume of the can. Round to the nearest tenth.|
Practice Test Answers
|1. .276 grams||2. 23760 feet||3. 9.317 miles|
|4. 211 minutes, 3 hours and 31 minutes||5. 95°F||6. 160 centimetres|
|7. 2,200 square centimetres||8. 11 feet, 9 feet||9. 282.6 inches|
|10. 201 feet||11. 1,440 cubic feet||12. 10.3 square inches|
|13. 31,400 cubic inches||14. a) 534.1 square inches b) 1335 cubic inches|