{"id":334,"date":"2020-11-26T13:41:21","date_gmt":"2020-11-26T18:41:21","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/pressbookbccampussmlt1\/chapter\/frustum-of-a-cone\/"},"modified":"2023-03-17T13:17:47","modified_gmt":"2023-03-17T17:17:47","slug":"frustum-of-a-cone","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/pressbookbccampussmlt1\/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=\"528\"]elevation view[\/pb_glossary]<\/strong>, including the <strong>[pb_glossary id=\"535\"]apex[\/pb_glossary] point<\/strong>.<strong><img class=\"wp-image-324 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/geoconst\/wp-content\/uploads\/sites\/1907\/2021\/07\/Step-1_1-16.gif\" alt=\"\" width=\"1000\" height=\"350\" \/><\/strong><\/li>\r\n \t<li><strong>[pb_glossary id=\"533\"]Profile[\/pb_glossary]<\/strong> the base of the elevation view and divide it into 6 equal parts.<img class=\"wp-image-325 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/geoconst\/wp-content\/uploads\/sites\/1907\/2023\/03\/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-326 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/geoconst\/wp-content\/uploads\/sites\/1907\/2023\/03\/Step-3_1-12.gif\" alt=\"\" width=\"1000\" height=\"350\" \/><\/li>\r\n \t<li>Project the <strong>[pb_glossary id=\"527\"]element lines[\/pb_glossary]<\/strong> from the base to the apex of the cone.\r\n<img class=\"wp-image-327 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/geoconst\/wp-content\/uploads\/sites\/1907\/2023\/03\/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-328 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/geoconst\/wp-content\/uploads\/sites\/1907\/2023\/03\/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=\"536\"]slant height[\/pb_glossary]<\/strong>\u00a0from the elevation view and swing an arc from the radius point.<strong><img class=\"wp-image-329 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/geoconst\/wp-content\/uploads\/sites\/1907\/2023\/03\/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-330 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/geoconst\/wp-content\/uploads\/sites\/1907\/2023\/03\/Step-7_2.gif\" alt=\"\" width=\"1000\" height=\"500\" \/><\/strong><\/li>\r\n \t<li>Along the <strong>[pb_glossary id=\"537\"]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-331 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/geoconst\/wp-content\/uploads\/sites\/1907\/2023\/03\/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-332 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/geoconst\/wp-content\/uploads\/sites\/1907\/2023\/03\/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-333 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/geoconst\/wp-content\/uploads\/sites\/1907\/2023\/03\/Step-10_2.gif\" alt=\"\" width=\"1000\" height=\"500\" \/><\/li>\r\n<\/ol>\r\nhttps:\/\/www.youtube.com\/watch?v=ptCT8ZeJsdQ&amp;list=PL0YcC46LnT8di2DsnBZrMgeEtso_LWIHL&amp;index=9\r\n\r\n&nbsp;","rendered":"<ol>\n<li>Draw an <strong><a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_334_528\">elevation view<\/a><\/strong>, including the <strong><a class=\"glossary-term\" aria-haspopup=\"dialog\" aria-describedby=\"definition\" href=\"#term_334_535\">apex<\/a> point<\/strong>.<strong><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-324 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/geoconst\/wp-content\/uploads\/sites\/1907\/2021\/07\/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_334_533\">Profile<\/a><\/strong> the base of the elevation view and divide it into 6 equal parts.<img loading=\"lazy\" decoding=\"async\" class=\"wp-image-325 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/geoconst\/wp-content\/uploads\/sites\/1907\/2023\/03\/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-326 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/geoconst\/wp-content\/uploads\/sites\/1907\/2023\/03\/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_334_527\">element lines<\/a><\/strong> from the base to the apex of the cone.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"wp-image-327 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/geoconst\/wp-content\/uploads\/sites\/1907\/2023\/03\/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-328 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/geoconst\/wp-content\/uploads\/sites\/1907\/2023\/03\/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_334_536\">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-329 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/geoconst\/wp-content\/uploads\/sites\/1907\/2023\/03\/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-330 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/geoconst\/wp-content\/uploads\/sites\/1907\/2023\/03\/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_334_537\">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-331 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/geoconst\/wp-content\/uploads\/sites\/1907\/2023\/03\/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-332 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/geoconst\/wp-content\/uploads\/sites\/1907\/2023\/03\/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-333 size-full aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/geoconst\/wp-content\/uploads\/sites\/1907\/2023\/03\/Step-10_2.gif\" alt=\"\" width=\"1000\" height=\"500\" \/><\/li>\n<\/ol>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Frustum of a Cone\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/ptCT8ZeJsdQ?list=PL0YcC46LnT8di2DsnBZrMgeEtso_LWIHL\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<div class=\"glossary\"><span class=\"screen-reader-text\" id=\"definition\">definition<\/span><template id=\"term_334_528\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_334_528\"><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_334_535\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_334_535\"><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_334_533\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_334_533\"><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_334_527\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_334_527\"><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_334_536\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_334_536\"><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_334_537\"><div class=\"glossary__definition\" role=\"dialog\" data-id=\"term_334_537\"><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":1078,"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-334","chapter","type-chapter","status-publish","hentry"],"part":285,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/pressbookbccampussmlt1\/wp-json\/pressbooks\/v2\/chapters\/334","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/pressbookbccampussmlt1\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/pressbookbccampussmlt1\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/pressbookbccampussmlt1\/wp-json\/wp\/v2\/users\/1078"}],"version-history":[{"count":3,"href":"https:\/\/pressbooks.bccampus.ca\/pressbookbccampussmlt1\/wp-json\/pressbooks\/v2\/chapters\/334\/revisions"}],"predecessor-version":[{"id":607,"href":"https:\/\/pressbooks.bccampus.ca\/pressbookbccampussmlt1\/wp-json\/pressbooks\/v2\/chapters\/334\/revisions\/607"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/pressbookbccampussmlt1\/wp-json\/pressbooks\/v2\/parts\/285"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/pressbookbccampussmlt1\/wp-json\/pressbooks\/v2\/chapters\/334\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/pressbookbccampussmlt1\/wp-json\/wp\/v2\/media?parent=334"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/pressbookbccampussmlt1\/wp-json\/pressbooks\/v2\/chapter-type?post=334"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/pressbookbccampussmlt1\/wp-json\/wp\/v2\/contributor?post=334"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/pressbookbccampussmlt1\/wp-json\/wp\/v2\/license?post=334"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}