{"id":246,"date":"2019-06-26T23:10:36","date_gmt":"2019-06-26T23:10:36","guid":{"rendered":"http:\/\/funfacts.104.42.120.246.xip.io\/?page_id=246"},"modified":"2019-12-20T22:47:29","modified_gmt":"2019-12-20T22:47:29","slug":"right-double-cone","status":"publish","type":"page","link":"https:\/\/math.hmc.edu\/funfacts\/right-double-cone\/","title":{"rendered":"Right Double Cone"},"content":{"rendered":"\n<div class=\"wp-block-image\"><figure class=\"alignright\"><img loading=\"lazy\" decoding=\"async\" width=\"271\" height=\"140\" data-attachment-id=\"1611\" data-permalink=\"https:\/\/math.hmc.edu\/funfacts\/right-double-cone\/10003-3-1\/\" data-orig-file=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/12\/10003.3.1.gif\" data-orig-size=\"271,140\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;,&quot;orientation&quot;:&quot;0&quot;}\" data-image-title=\"10003.3.1\" data-image-description=\"\" data-image-caption=\"\" data-medium-file=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/12\/10003.3.1.gif\" data-large-file=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/12\/10003.3.1.gif\" src=\"https:\/\/math.hmc.edu\/funfacts\/wp-content\/uploads\/sites\/4\/2019\/12\/10003.3.1.gif\" alt=\"\" class=\"wp-image-1611\"\/><\/figure><\/div>\n\n\n\n<p>Take a solid cylinder of radius R and height 2R. Remove the right &#8220;double cone&#8221; which passes through the center of the solid cylinder and extends meet the circular discs on the top and bottom of the cylinder. See Figure 1.<\/p>\n\n\n\n<p>The volume of the remaining object and the volume of a sphere of radius R are the same!<\/p>\n\n\n\n<p><strong>Presentation&nbsp;Suggestions:<\/strong><br>Pictures, pictures!<\/p>\n\n\n\n<p><strong>The\u00a0Math\u00a0Behind\u00a0the\u00a0Fact:<\/strong><br>Using\u00a0Cavalieri&#8217;s principle\u00a0is perhaps the most effective way to prove this in a\u00a0multivariable calculus\u00a0course.<\/p>\n\n\n\n<p><strong>How to Cite this Page:<\/strong>&nbsp;<br>Su, Francis E., et al. &#8220;Right Double Cone.&#8221;&nbsp;<em>Math Fun Facts<\/em>. &lt;http:\/\/www.math.hmc.edu\/funfacts&gt;.<\/p>\n\n\n\n<p><strong>Fun Fact suggested by<\/strong>:<br>Jorge Aarao&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Take a solid cylinder of radius R and height 2R. Remove the right &#8220;double cone&#8221; which passes through the center&#46;&#46;&#46;<\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"tags":[20,7,3,123,44],"class_list":["post-246","page","type-page","status-publish","hentry","tag-analysis","tag-calculus","tag-easy","tag-multivariable-calculus","tag-sphere"],"jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/246","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/comments?post=246"}],"version-history":[{"count":4,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/246\/revisions"}],"predecessor-version":[{"id":1612,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/pages\/246\/revisions\/1612"}],"wp:attachment":[{"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/media?parent=246"}],"wp:term":[{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/math.hmc.edu\/funfacts\/wp-json\/wp\/v2\/tags?post=246"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}