{"id":3358,"date":"2023-10-28T11:03:06","date_gmt":"2023-10-28T15:03:06","guid":{"rendered":"https:\/\/josmfs.net\/?p=3358"},"modified":"2023-10-28T11:03:06","modified_gmt":"2023-10-28T15:03:06","slug":"maximized-box-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2023\/10\/28\/maximized-box-problem\/","title":{"rendered":"Maximized Box Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-3357\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/10\/Maximized-Box-Fig2.jpg\" alt=\"\" width=\"200\" height=\"200\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/10\/Maximized-Box-Fig2.jpg 402w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/10\/Maximized-Box-Fig2-300x300.jpg 300w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/10\/Maximized-Box-Fig2-150x150.jpg 150w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>This problem is from Colin Hughes\u2019s <em>Maths Challenge<\/em> website (mathschallenge.net).<\/p>\n<p>\u201cFour corners measuring <em>x <\/em>by <em>x <\/em>are removed from a sheet of material that measures <em>a <\/em>by <em>a <\/em>to make a square based open-top box.\u00a0 Prove that the volume of the box is maximised iff the area of the base is equal to the area of the four sides.\u201d<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/10\/Maximized-Box-230831.pdf\">Maximized Box Problem<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This problem is from Colin Hughes\u2019s Maths Challenge website (mathschallenge.net). \u201cFour corners measuring x by x are removed from a sheet of material that measures a by a to make a square based open-top box.\u00a0 Prove that the volume of the box is maximised iff the area of the base is equal to the area [&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":[32,151],"class_list":["post-3358","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-calculus","tag-colin-hughes"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3358","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=3358"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3358\/revisions"}],"predecessor-version":[{"id":3359,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3358\/revisions\/3359"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=3358"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=3358"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=3358"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}