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Math Help - Cylindrical and Spherical coords volume

  1. #1
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    Apr 2011
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    Spherical coords volume

    Hello,

    I keep getting this volume wrong by a factor of 4... I keep ending up with 16 \ pi \sqrt{3} instead of 4\pi \sqrt{3}. Could someone please tell me what's wrong in my integral?

    Question is: Find the volume that is inside x^2+y^2+z^2=4 but outside x^2+y^2=1.

    My integral is \int_0^{2\pi} \int_{\frac{\pi}{6}}^{\frac{5\pi}{6}} \int_{\frac{1}{\sin \phi}}^2 \rho^2 \sin \phi d \phi d \rho d \theta.

    Thanks

    EDIT: I've figured out how to do this problem... Took quite a bit though... So I don't need help on this problem anymore
    Last edited by minifhncc; May 7th 2011 at 06:26 AM.
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  2. #2
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    Apr 2011
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    I can do this using cylindrical shells and cylindrical coordinates but I cannot doing it using spherical coordinate (which the method requested by the question).

    I really cannot see how my limits are wrong, especially given that these two methods do work. Could someone please point out why my method in the first post using spherical coordinates yields the wrong answer? It's driving me crazy.

    Thanks heaps
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