A right circular cone is to be inscribed in another right circular cone of volume 4m3 and altitude 5m, with the same axis and with the vertex of the inner cone touching the base of the outer cone.
What must be the altitude of the inscribed cone in order to have the largest possible volume?
Calculus 1
2013-11-23 5:35 am
回答 (1)
2013-11-24 2:29 am
✔ 最佳答案
圖片參考：http://imgcld.yimg.com/8/n/HA06881079/o/20131123181808.jpg
Let OF=h, AF=5-h, then
AF²:OA²=πEF²: πOC²
(5-h)²: 25=πEF²: 12/5
πEF² = (12/125)(5-h)²
V=(1/3)h*πEF²=(4π/125)h(5-h)², 0 < h < 5
dV/dh=(4π/125)[ (5-h)²- 2h(5-h)]
=(4π/125) (5-h) (5-3h)
when 5/3 < h < 5, dV/dh < 0, V is decreasing
when 0 < h < 5/3, V is increasing
so, when h= 5/3 meters, the volume of the inner cone is max.
收錄日期: 2021-05-01 18:38:16
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20131122000051KK00167