{"id":1732,"date":"2020-08-22T08:17:22","date_gmt":"2020-08-22T12:17:22","guid":{"rendered":"http:\/\/josmfs.net\/?p=1732"},"modified":"2024-04-08T12:41:24","modified_gmt":"2024-04-08T16:41:24","slug":"another-cube-slice-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2020\/08\/22\/another-cube-slice-problem\/","title":{"rendered":"Another Cube Slice Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-1728\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/08\/Another-Cube-Slice-Fig.jpg\" alt=\"\" width=\"206\" height=\"256\" \/>This is a problem from the UKMT Senior Challenge for 2019.\u00a0 (It has been slightly edited to reflect the colors I added to the diagram.)<\/p>\n<p>\u201cThe edge-length of the solid cube shown is 2.\u00a0 A single plane cut goes through the points Y, T, V and W which are midpoints of the edges of the cube, as shown.<\/p>\n<p>What is the area of the cross-section?<\/p>\n<p style=\"text-align: center;\">A<span style=\"color: #ffffff;\">_<\/span>\u221a3<span style=\"color: #ffffff;\">_____<\/span>B<span style=\"color: #ffffff;\">_<\/span>3\u221a3<span style=\"color: #ffffff;\">_____<\/span>C<span style=\"color: #ffffff;\">_<\/span>6<span style=\"color: #ffffff;\">_____<\/span>D<span style=\"color: #ffffff;\">_<\/span>6\u221a3<span style=\"color: #ffffff;\">_____<\/span>E<span style=\"color: #ffffff;\">_<\/span>8\u201d<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Another-Cube-Slice-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/08\/Another-Cube-Slice-Problem-200804.pdf\">Another Cube Slice Problem<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is a problem from the UKMT Senior Challenge for 2019.\u00a0 (It has been slightly edited to reflect the colors I added to the diagram.) \u201cThe edge-length of the solid cube shown is 2.\u00a0 A single plane cut goes through the points Y, T, V and W which are midpoints of the edges of the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[13,83],"class_list":["post-1732","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-plane-geometry","tag-ukmt-challenge"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1732","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=1732"}],"version-history":[{"count":3,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1732\/revisions"}],"predecessor-version":[{"id":3736,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1732\/revisions\/3736"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=1732"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=1732"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=1732"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}