http://i150.photobucket.com/albums/s87/mllokloks/prove.jpg
半徑為R的球體內切於體積為V的直立圓錐體,其中連接球心和圓錐體底邊上任意一點的直綫與底的角為 theta
Prove V = (1/3)(pi)(R^3)(tan theta)(cot^3 theta)
Proof Question
2007-11-10 4:45 am
回答 (1)
2007-11-11 2:11 am
✔ 最佳答案
設直立圓錐體半徑r﹐高hR/r=tan θ
r=R/tan θ
又
h/r=tan 2θ
h=rtan 2θ
所以
V
= (1/3)(π)(r^2)h
= (1/3)(π)(R^2/tan^2 θ )(R/tan θ)(tan 2θ)
= (1/3)(π)(R^3 cot^3 θ )(tan 2θ)
收錄日期: 2021-04-25 16:53:44
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20071109000051KK03251