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Math Help - Calculate the volume of a sphere

  1. #1
    MHF Contributor arbolis's Avatar
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    Calculate the volume of a sphere

    I set up myself to calculate the volume of a sphere of radius r using spherical coordinates.
    I found that V=\frac{r^2\pi}{2}. So I think I set up badly the triple integral : V=\int_0^{2\pi}\int_0^{\pi}\int_0^r \rho \sin ^2 (\phi) d\rho d\phi d\theta.
    Maybe I made an error with the order of integration, but I don't see it.
    Edit : I just saw my error. I integrated \rho \sin ^2 \phi instead of \rho ^2 \sin \phi.
    Last edited by arbolis; June 18th 2009 at 06:12 PM.
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  2. #2
    MHF Contributor Bruno J.'s Avatar
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    Shouldn't you have dV = \rho^2 \sin \phi\: d\rho\:  d\phi\:  d\theta ?

    Also your \rho is confusing; r is the standard notation.
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