(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

For a sphere of radius r find the volume of the cap of height h.

2. Relevant equations

3. The attempt at a solution

I can get it down to [tex]V \ = \ \pi \int_{r-h}^r (\pi r^2 - \pi y^2)dy \ = \ \pi {\left[(r^2y-\dfrac{1}{3} y^3) \right] }_{r-h}^r[/tex]

I expanded this to [tex]V=\pi (-\dfrac{2}{3} r^3+2r^2h-rh^2-\dfrac{1}{3}h^3)[/tex]

but the book has [tex]V=\pi h^2(r-\dfrac{1}{3} h)[/tex]

What am I missing/doing wrong?

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# Integral Volume of Sphere

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