{"id":317,"date":"2021-08-13T13:22:35","date_gmt":"2021-08-13T17:22:35","guid":{"rendered":"https:\/\/opentextbc.ca\/patterndevelopment\/chapter\/frustum-of-a-cone\/"},"modified":"2023-01-24T13:17:59","modified_gmt":"2023-01-24T18:17:59","slug":"frustum-of-a-cone","status":"web-only","type":"chapter","link":"https:\/\/opentextbc.ca\/patterndevelopment\/chapter\/frustum-of-a-cone\/","title":{"raw":"Frustum of a Cone","rendered":"Frustum of a Cone"},"content":{"raw":"<ol>\r\n \t<li>Draw an <strong>[pb_glossary id=\"499\"]elevation view[\/pb_glossary]<\/strong>, including the <strong>[pb_glossary id=\"480\"]apex[\/pb_glossary] point<\/strong>.<strong><img class=\"wp-image-809 size-full aligncenter\" src=\"https:\/\/opentextbc.ca\/patterndevelopment\/wp-content\/uploads\/sites\/359\/2021\/08\/Step-1_1-16.gif\" alt=\"\" width=\"1000\" height=\"350\" \/><\/strong><\/li>\r\n \t<li><strong>[pb_glossary id=\"478\"]Profile[\/pb_glossary]<\/strong> the base of the elevation view and divide it into 6 equal parts.<img class=\"wp-image-810 size-full aligncenter\" src=\"https:\/\/opentextbc.ca\/patterndevelopment\/wp-content\/uploads\/sites\/359\/2021\/08\/Step-2_1-15.gif\" alt=\"\" width=\"1000\" height=\"350\" \/><\/li>\r\n \t<li>Label the profile from 1 to 7 and project the divisions vertically into the base of the cone.<img class=\"wp-image-811 size-full aligncenter\" src=\"https:\/\/opentextbc.ca\/patterndevelopment\/wp-content\/uploads\/sites\/359\/2021\/08\/Step-3_1-12.gif\" alt=\"\" width=\"1000\" height=\"350\" \/><\/li>\r\n \t<li>Project the <strong>[pb_glossary id=\"507\"]element lines[\/pb_glossary]<\/strong> from the base to the apex of the cone.\r\n<img class=\"wp-image-814 size-full aligncenter\" src=\"https:\/\/opentextbc.ca\/patterndevelopment\/wp-content\/uploads\/sites\/359\/2021\/08\/Step-4-16.gif\" alt=\"\" width=\"1000\" height=\"350\" \/><\/li>\r\n \t<li>Locate a radius point where you want to develop the pattern.<img class=\"wp-image-817 size-full aligncenter\" src=\"https:\/\/opentextbc.ca\/patterndevelopment\/wp-content\/uploads\/sites\/359\/2021\/08\/Step-5_1-12.gif\" alt=\"\" width=\"1000\" height=\"500\" \/><\/li>\r\n \t<li>With your compass, take the large\u00a0<strong>[pb_glossary id=\"481\"]slant height[\/pb_glossary]<\/strong>\u00a0from the elevation view and swing an arc from the radius point.<strong><img class=\"wp-image-828 size-full aligncenter\" src=\"https:\/\/opentextbc.ca\/patterndevelopment\/wp-content\/uploads\/sites\/359\/2021\/08\/Step-6_2-1.gif\" alt=\"\" width=\"1000\" height=\"500\" \/><\/strong><\/li>\r\n \t<li>Set your compass to the small\u00a0slant height and swing it from the same radius point.<strong><img class=\"wp-image-824 size-full aligncenter\" src=\"https:\/\/opentextbc.ca\/patterndevelopment\/wp-content\/uploads\/sites\/359\/2021\/08\/Step-7_2.gif\" alt=\"\" width=\"1000\" height=\"500\" \/><\/strong><\/li>\r\n \t<li>Along the <strong>[pb_glossary id=\"482\"]stretch-out[\/pb_glossary]<\/strong> (large) arc, establish a starting point for the pattern and draw a line back to the radius point.<strong><img class=\"wp-image-825 size-full aligncenter\" src=\"https:\/\/opentextbc.ca\/patterndevelopment\/wp-content\/uploads\/sites\/359\/2021\/08\/Step-8_2-1.gif\" alt=\"\" width=\"1000\" height=\"500\" \/><\/strong><\/li>\r\n \t<li>Set your compass to a step-off. From your starting point, swing it 12 times along the stretch-out arc. <strong>In this case, this must be done on the large or stretch-out arc because that is where the step-off is taken from.<img class=\"wp-image-826 size-full aligncenter\" src=\"https:\/\/opentextbc.ca\/patterndevelopment\/wp-content\/uploads\/sites\/359\/2021\/08\/Step-9_2.gif\" alt=\"\" width=\"1000\" height=\"500\" \/><\/strong><\/li>\r\n \t<li>Connect the last point back to the radius point to complete the pattern.<img class=\"wp-image-827 size-full aligncenter\" src=\"https:\/\/opentextbc.ca\/patterndevelopment\/wp-content\/uploads\/sites\/359\/2021\/08\/Step-10_2.gif\" alt=\"\" width=\"1000\" height=\"500\" \/><\/li>\r\n<\/ol>\r\nhttps:\/\/media.bccampus.ca\/id\/0_59h7c0p4?width=608&amp;height=402&amp;playerId=23449753\r\n\r\n&nbsp;","rendered":"<ol>\n<li>Draw an <strong><a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_317_499\">elevation view<\/a><\/strong>, including the <strong><a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_317_480\">apex<\/a> point<\/strong>.<strong><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-809 size-full aligncenter\" src=\"https:\/\/opentextbc.ca\/patterndevelopment\/wp-content\/uploads\/sites\/359\/2021\/08\/Step-1_1-16.gif\" alt=\"\" width=\"1000\" height=\"350\" \/><\/strong><\/li>\n<li><strong><a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_317_478\">Profile<\/a><\/strong> the base of the elevation view and divide it into 6 equal parts.<img loading=\"lazy\" decoding=\"async\" class=\"wp-image-810 size-full aligncenter\" src=\"https:\/\/opentextbc.ca\/patterndevelopment\/wp-content\/uploads\/sites\/359\/2021\/08\/Step-2_1-15.gif\" alt=\"\" width=\"1000\" height=\"350\" \/><\/li>\n<li>Label the profile from 1 to 7 and project the divisions vertically into the base of the cone.<img loading=\"lazy\" decoding=\"async\" class=\"wp-image-811 size-full aligncenter\" src=\"https:\/\/opentextbc.ca\/patterndevelopment\/wp-content\/uploads\/sites\/359\/2021\/08\/Step-3_1-12.gif\" alt=\"\" width=\"1000\" height=\"350\" \/><\/li>\n<li>Project the <strong><a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_317_507\">element lines<\/a><\/strong> from the base to the apex of the cone.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"wp-image-814 size-full aligncenter\" src=\"https:\/\/opentextbc.ca\/patterndevelopment\/wp-content\/uploads\/sites\/359\/2021\/08\/Step-4-16.gif\" alt=\"\" width=\"1000\" height=\"350\" \/><\/li>\n<li>Locate a radius point where you want to develop the pattern.<img loading=\"lazy\" decoding=\"async\" class=\"wp-image-817 size-full aligncenter\" src=\"https:\/\/opentextbc.ca\/patterndevelopment\/wp-content\/uploads\/sites\/359\/2021\/08\/Step-5_1-12.gif\" alt=\"\" width=\"1000\" height=\"500\" \/><\/li>\n<li>With your compass, take the large\u00a0<strong><a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_317_481\">slant height<\/a><\/strong>\u00a0from the elevation view and swing an arc from the radius point.<strong><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-828 size-full aligncenter\" src=\"https:\/\/opentextbc.ca\/patterndevelopment\/wp-content\/uploads\/sites\/359\/2021\/08\/Step-6_2-1.gif\" alt=\"\" width=\"1000\" height=\"500\" \/><\/strong><\/li>\n<li>Set your compass to the small\u00a0slant height and swing it from the same radius point.<strong><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-824 size-full aligncenter\" src=\"https:\/\/opentextbc.ca\/patterndevelopment\/wp-content\/uploads\/sites\/359\/2021\/08\/Step-7_2.gif\" alt=\"\" width=\"1000\" height=\"500\" \/><\/strong><\/li>\n<li>Along the <strong><a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_317_482\">stretch-out<\/a><\/strong> (large) arc, establish a starting point for the pattern and draw a line back to the radius point.<strong><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-825 size-full aligncenter\" src=\"https:\/\/opentextbc.ca\/patterndevelopment\/wp-content\/uploads\/sites\/359\/2021\/08\/Step-8_2-1.gif\" alt=\"\" width=\"1000\" height=\"500\" \/><\/strong><\/li>\n<li>Set your compass to a step-off. From your starting point, swing it 12 times along the stretch-out arc. <strong>In this case, this must be done on the large or stretch-out arc because that is where the step-off is taken from.<img loading=\"lazy\" decoding=\"async\" class=\"wp-image-826 size-full aligncenter\" src=\"https:\/\/opentextbc.ca\/patterndevelopment\/wp-content\/uploads\/sites\/359\/2021\/08\/Step-9_2.gif\" alt=\"\" width=\"1000\" height=\"500\" \/><\/strong><\/li>\n<li>Connect the last point back to the radius point to complete the pattern.<img loading=\"lazy\" decoding=\"async\" class=\"wp-image-827 size-full aligncenter\" src=\"https:\/\/opentextbc.ca\/patterndevelopment\/wp-content\/uploads\/sites\/359\/2021\/08\/Step-10_2.gif\" alt=\"\" width=\"1000\" height=\"500\" \/><\/li>\n<\/ol>\n<p><iframe loading=\"lazy\" id=\"kaltura_player\" title=\"Radial Line - Frustum of a Cone\" src=\"https:\/\/api.ca.kaltura.com\/p\/148\/sp\/14800\/embedIframeJs\/uiconf_id\/23449753\/partner_id\/148?iframeembed=true&#38;playerId=kaltura_player&#38;entry_id=0_59h7c0p4&#38;flashvars[leadWithHTML5]=true&#38;flashvars[streamerType]=auto&#38;flashvars[localizationCode]=en&#38;flashvars[sideBarContainer.plugin]=true&#38;flashvars[sideBarContainer.position]=left&#38;flashvars[sideBarContainer.clickToClose]=true&#38;flashvars[chapters.plugin]=true&#38;flashvars[chapters.layout]=vertical&#38;flashvars[chapters.thumbnailRotator]=false&#38;flashvars[streamSelector.plugin]=true&#38;flashvars[EmbedPlayer.SpinnerTarget]=videoHolder&#38;flashvars[dualScreen.plugin]=true&#38;flashvars[Kaltura.addCrossoriginToIframe]=true&#38;wid=0_p5ybvfoa\" width=\"608\" height=\"402\" allowfullscreen=\"allowfullscreen\" sandbox=\"allow-downloads allow-forms allow-same-origin allow-scripts allow-top-navigation allow-pointer-lock allow-popups allow-modals allow-orientation-lock allow-popups-to-escape-sandbox allow-presentation allow-top-navigation-by-user-activation\" frameborder=\"0\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<div class=\"glossary\"><span class=\"screen-reader-text\" id=\"definition\">definition<\/span><template id=\"term_317_499\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_317_499\"><div tabindex=\"-1\"><p>looking at the front or side of something, to have elevation (height), 2D<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_317_480\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_317_480\"><div tabindex=\"-1\"><p>the intersection point of a cone, as seen in the elevation view<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_317_478\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_317_478\"><div tabindex=\"-1\"><p>a half of a plan view, drawn on the outside of an object<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_317_507\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_317_507\"><div tabindex=\"-1\"><p>a line representing an edge or bend<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_317_481\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_317_481\"><div tabindex=\"-1\"><p>the hypotenuse of a cone, outside edge. The slant height is always a true length in the elevation view<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><template id=\"term_317_482\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_317_482\"><div tabindex=\"-1\"><p>the angle or arc which encompasses a radial line pattern<\/p>\n<\/div><button><span aria-hidden=\"true\">&times;<\/span><span class=\"screen-reader-text\">Close definition<\/span><\/button><\/div><\/template><\/div>","protected":false},"author":90,"menu_order":5,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-317","chapter","type-chapter","status-web-only","hentry"],"part":272,"_links":{"self":[{"href":"https:\/\/opentextbc.ca\/patterndevelopment\/wp-json\/pressbooks\/v2\/chapters\/317","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/opentextbc.ca\/patterndevelopment\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/opentextbc.ca\/patterndevelopment\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/opentextbc.ca\/patterndevelopment\/wp-json\/wp\/v2\/users\/90"}],"version-history":[{"count":2,"href":"https:\/\/opentextbc.ca\/patterndevelopment\/wp-json\/pressbooks\/v2\/chapters\/317\/revisions"}],"predecessor-version":[{"id":621,"href":"https:\/\/opentextbc.ca\/patterndevelopment\/wp-json\/pressbooks\/v2\/chapters\/317\/revisions\/621"}],"part":[{"href":"https:\/\/opentextbc.ca\/patterndevelopment\/wp-json\/pressbooks\/v2\/parts\/272"}],"metadata":[{"href":"https:\/\/opentextbc.ca\/patterndevelopment\/wp-json\/pressbooks\/v2\/chapters\/317\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/opentextbc.ca\/patterndevelopment\/wp-json\/wp\/v2\/media?parent=317"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/opentextbc.ca\/patterndevelopment\/wp-json\/pressbooks\/v2\/chapter-type?post=317"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/opentextbc.ca\/patterndevelopment\/wp-json\/wp\/v2\/contributor?post=317"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/opentextbc.ca\/patterndevelopment\/wp-json\/wp\/v2\/license?post=317"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}