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Math Help - Mass in a spherical shell

  1. #1
    nbram87
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    Mass in a spherical shell

    Find the mass of the portion lying in the first octant of the spherical shell between the two spheres with radii a less than b if the density at point (x,y,z) is x. Thanks for anybody's help!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by nbram87 View Post
    Find the mass of the portion lying in the first octant of the spherical shell between the two spheres with radii a less than b if the density at point (x,y,z) is x. Thanks for anybody's help!
    Use spherical polars, then x=\rho \sin(\phi)) \cos(\theta)) , so the required mass is:

    M=\int_V x ~dV=\int_{\rho=a}^b \int_{\phi=0}^{\pi/2} \int_{\theta=0}^{\pi/2} x~ \rho^2 \sin(\phi) d\rho~ d\phi~ d\theta

    RonL
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