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Math Help - Volume of solid inside 2 spheres

  1. #1
    pearlman
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    Volume of solid inside 2 spheres

    Hi everyone, I need help with this task:
    Find the volume of solid inside both of the spheres
    \rho = 2\sqrt{2} cos \phi and \rho = 2

    thank you in advance for any help with this
    Last edited by pearlman; November 25th 2007 at 07:51 AM.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by pearlman View Post
    Hi everyone, I need help with this task:
    Find the volume of solid inside both of the spheres
    \rho = 2\sqrt{2} cos \phi and \rho = 2

    thank you in advance for any help with this
    Not that I'm good at answering these in any case, but I note that \rho = 2\sqrt{2} cos(\phi) is not a sphere.

    -Dan
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  3. #3
    Eater of Worlds
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    I believe it may be a sphere. Just not centered at the origin.

    They intersect when 2=2\sqrt{2}cos{\phi}

    cos^{-1}(\frac{1}{\sqrt{2}})=\frac{\pi}{4}

    \int_{0}^{2{\pi}}\int_{0}^{\frac{\pi}{4}}\int_{0}^  {2}{\rho}^{2}sin^{2}{\phi}d{\rho}d{\phi}d{\theta}
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