{"id":829,"date":"2019-03-28T10:04:53","date_gmt":"2019-03-28T14:04:53","guid":{"rendered":"http:\/\/josmfs.net\/?p=829"},"modified":"2024-04-14T11:13:04","modified_gmt":"2024-04-14T15:13:04","slug":"conical-bottle-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2019\/03\/28\/conical-bottle-problem\/","title":{"rendered":"Conical Bottle Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-3865\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Conical-Bottle-Fig2.jpg\" alt=\"\" width=\"200\" height=\"117\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Conical-Bottle-Fig2.jpg 402w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Conical-Bottle-Fig2-300x175.jpg 300w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>I was astonished that this problem was suitable for 8th graders. First of all the formula for the volume of a cone is one of the least-remembered of formulas, and I certainly never remember it. So my only viable approach was calculus, which is probably not a suitable solution for an 8th grader.<\/p>\n<p>Presh Talwalkar: \u201cThis was sent to me as a competition problem for 8th graders, so it would be a challenge problem for students aged 12 to 13. When a conical bottle rests on its flat base, the water in the bottle is 8 cm from its vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle? (Note \u201cconical\u201d refers to a right circular cone as is common usage.) I at first thought this problem was impossible. But it actually can be solved.\u201d<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Conical-Bottle-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2019\/03\/Conical-Bottle-Problem-181106.pdf\">Conical Bottle Problem<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I was astonished that this problem was suitable for 8th graders. First of all the formula for the volume of a cone is one of the least-remembered of formulas, and I certainly never remember it. So my only viable approach was calculus, which is probably not a suitable solution for an 8th grader. Presh Talwalkar: [&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":[32,13,17],"class_list":["post-829","post","type-post","status-publish","format-standard","hentry","category-math-inquiries","tag-calculus","tag-plane-geometry","tag-presh-talwalkar"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/829","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=829"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/829\/revisions"}],"predecessor-version":[{"id":3867,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/829\/revisions\/3867"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=829"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=829"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=829"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}