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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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