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Math Help - cylindrical coordinates = triple integral

  1. #1
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    Question cylindrical coordinates = triple integral

    use cylindrical coordinates to find the centroid of the solid that is bounded above by the sphere x^2 +y^2 +z^2 =2 and below by the paraboloid z=x^2 +y^2.

    Thank you very much.
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  2. #2
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    You're breaking my heart, kc. You simply MUST be able to do this one.

    Hint: r^{2} = x^{2} + y^{2}

    Come on, show your stuff! You CAN do it.
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  3. #3
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    Smile

    TKHunny, I am not that great as you thought!


    Luckily, I think I just solved this question. I have
    r is from 0 to 1
    theta is from 0 to 2 pi
    z is from r^2 to sqrt(2-r^2)

    V =[ (8sqrt(2)-7)pi]/6

    By symmetry, x bar = y bar

    z bar = 7/[16sqrt(2) -14]

    therefore the centroid is (0,0,7/[16sqrt(2) -14] )

    I hope that I am right since the answer is correct as the book given.
    Last edited by kittycat; September 17th 2007 at 11:08 AM.
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  4. #4
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    If only you had shown us how you found your limits for 'r', then it would have been almost perfect.
    You also should have stated "x bar = y bar = 0". You left off the last part.

    Now that you have done this one so well, who's right about whether or not you can do it?
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