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Math Help - Volume cut out of a sphere

  1. #1
    wozzup
    Guest

    Volume cut out of a sphere

    Hello,

    i need some help.

    My problem is:

    "Find the volume cut out of the sphere x^2 + y^2 + z^2 = 4a^2 by the cylinder x^2 + y^2 = 2ax."

    I turned these equations to polar coordinates: z = 4a^2 - r^2 (this is under a root sign) and r = 2acosx (x is theta here).

    The integral I set up is a double integral with limits from -pi/2 to pi/2 and the second integral from 0 to 2acosx and the integrand is (4a^2 - r^2)^0.5 r dr dx (where x is theta here).

    I have a negative result (-32a^3/9), which must be wrong?! can somebody show me the steps toward the solution?

    Thanks.
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  2. #2
    MHF Contributor
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    What was deficient about my previous reply? Don't solve for dt and make things negative. This is also something symmetries will solve for you. If you stay where things are positive, and multiply by some constant to cover the rest, errors of sign are much more difficult to create.

    S.O.S. Mathematics CyberBoard :: View topic - Volume cut out of sphere
    Last edited by TKHunny; September 9th 2007 at 08:45 PM. Reason: Add Link.
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