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Math Help - Derive the Volume of a Cap of a Sphere Using Integrals

  1. #1
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    Derive the Volume of a Cap of a Sphere Using Integrals

    Hey everyone, I'm trying to derive the formula for the volume of a cap of a sphere. The sphere has radius "r" and the height of JUST THE CAP is "h." The only thing that I can think to do is revolve an arbitrary 2D shape around the x-axis, making a cap with the limits of integration from r-h to r. It sounds very complicated though and I'm having lots of trouble with it. Can anyone give me some ideas? THanks
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  2. #2
    Eater of Worlds
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    It's not as bad as it seems.


    {\pi}\int_{r-h}^{r}(r^{2}-y^{2})dy
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