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Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決
Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決 
一題高中積分數學
Dec 16th 2014, 17:01

將一半徑為5cm的球,滾入桌面一個半徑為3cm的圓洞中,請問這個球在
桌面上的體積?
Sol
設最深pcm
3*3=p*(10-p)
p^2-10p+9=0
(p-1)(p-9)=0
p=1 or p=9(不合)
V=∫(-4 to 5)_π(25-x^2)dx
=25πx|(-4 to 5)-(π/3)x^3|(-4 to 5)
=225π-(π/3)(125+64)
=162π

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