{"id":2555,"date":"2022-01-22T07:59:40","date_gmt":"2022-01-22T12:59:40","guid":{"rendered":"https:\/\/josmfs.net\/?p=2555"},"modified":"2024-04-08T10:03:06","modified_gmt":"2024-04-08T14:03:06","slug":"another-christmas-tree-puzzle","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2022\/01\/22\/another-christmas-tree-puzzle\/","title":{"rendered":"Another Christmas Tree Puzzle"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2553\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/01\/Another-Christmas-Tree-Fig2.jpg\" alt=\"\" width=\"105\" height=\"223\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/01\/Another-Christmas-Tree-Fig2.jpg 259w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/01\/Another-Christmas-Tree-Fig2-142x300.jpg 142w\" sizes=\"auto, (max-width: 105px) 100vw, 105px\" \/>This is a belated Christmas puzzle from December 2019 <a href=\"https:\/\/twitter.com\/MEIMaths\/status\/1206514304544985093\">MathsMonday<\/a>.<\/p>\n<p>\u201cA Christmas tree is made by stacking successively smaller cones. The largest cone has a base of radius 1 unit and a height of 2 units. Each smaller cone has a radius 3\/4 of the previous cone and a height 3\/4 of the previous cone. Its base overlaps the previous cone, sitting at a height 3\/4 of the way up the previous cone.<\/p>\n<p>What are the dimensions of the smallest cone, by volume, that will contain the whole tree for any number of cones?\u201d<\/p>\n<p>Recall that the volume of a cone is \u03c0 r<sup>2 <\/sup>h\/3.<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Another-Christmas-Tree-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/01\/Another-Christmas-Tree-Puzzle-220121.pdf\">Another Christmas Tree Puzzle<\/a> for a solution.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is a belated Christmas puzzle from December 2019 MathsMonday. \u201cA Christmas tree is made by stacking successively smaller cones. The largest cone has a base of radius 1 unit and a height of 2 units. Each smaller cone has a radius 3\/4 of the previous cone and a height 3\/4 of the previous cone. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[213,230],"class_list":["post-2555","post","type-post","status-publish","format-standard","hentry","category-math-inquiries","tag-mathsmonday","tag-sequences-and-series"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2555","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=2555"}],"version-history":[{"count":4,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2555\/revisions"}],"predecessor-version":[{"id":3710,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2555\/revisions\/3710"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2555"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2555"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2555"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}