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Math Help - Need help with surface area of this sphere

  1. #1
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    Need help with surface area of this sphere

    i need to determine the surface area of the portion of the sphere x^2 + y^2 + z^2 = 16 that lies between the planes z=1 and z=2
    i have taken the derivatives with respect to x and y and have switched to polar coordinates and now i have the integral:
    \int \int {{(4/\sqrt(16-r^2)dA}}
    I am not sure what the limits of the integrals will be. But i am pretty sure the leftmost integral has the limits 0 to 2\pi. can someone help me figure out the limits of the integrals? thanks.
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  2. #2
    Eater of Worlds
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    If you sub in z=1 and z=2 into the sphere equation you get:

    r^{2}=15, \;\ r^{2}=12

    So, you get:

    \int_{0}^{2\pi}\int_{\sqrt{12}}^{\sqrt{15}}\frac{4  r}{\sqrt{16-r^{2}}}drd{\theta}

    =4\int_{0}^{2\pi}d{\theta}=8{\pi}
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