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Math Help - Triple Integral in Cylindrical Coordinates

  1. #1
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    Triple Integral in Cylindrical Coordinates

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

    I figured that \rho=Kr, so the integrand would be Kr^2. I think that my limits of integration are wrong. I got 0\leq\theta\leq2\pi, 0\leq r \leq a, -\sqrt{a-r^2} \leq z \leq \sqrt{a-r^2}
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by MathTooHard View Post
    Find the mass of a ball B given by x^2+y^2+z^2 \leq a^2 if the density at any point is proportional to its distance from the z-axis.

    I figured that \rho=Kr, so the integrand would be Kr^2. I think that my limits of integration are wrong. I got 0\leq\theta\leq2\pi, 0\leq r \leq a, -\sqrt{a-r^2} \leq z \leq \sqrt{a-r^2}
    The limits on z are incorrect...but you're very close. I'll give you a chance to see if you can spot your mistake. If you can't, reply back, and I'll help you.
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  3. #3
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    Oh wow, I can't believe I spent that much time agonizing over this problem. Thanks!
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  4. #4
    MHF Contributor matheagle's Avatar
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    wouldn't spherical be easier?
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  5. #5
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    It would indeed. I should have mentioned that my textbook specifically wanted cylindrical coordinates.
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