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Math Help - Finding Mass

  1. #1
    Junior Member
    Nov 2007

    Finding Mass

    I am having trouble with the following question:

    Find the mass of a ball B given by (x^2) + (y^2) + (z^2) <= (a^2) if the density at any point is proportional to its distance from the z-axis.

    Any ideas or help would be appreciated. Thanks!
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  2. #2
    MHF Contributor matheagle's Avatar
    Feb 2009
    You need to change variables. Rectangular is painful. The density here is
    kr=k\sqrt{x^2+y^2}=k\rho\sin\phi, but the k's cancel, so you can let k=1.
    Try spherical, where the Jacobian is \rho^2\sin\phi.
    If you're integating over the entire ball, then 0<\rho <a, 0<\theta <2\pi and 0<\phi<\pi.
    Last edited by matheagle; March 14th 2009 at 05:42 PM.
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