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Math Help - Area of a surface inside a cylinder

  1. #1
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    Question Area of a surface inside a cylinder

    Find the area of that part of the surface z = xy inside the cylinder x^2 +y^2 = a^2.

    Well I don't know what the surface looks like but I have an idea of what the cylinder looks like.

    It's like drawing a circle in the xy plane centered at the origin with radius a and pulling that circle in the z direction to create a cylinder.

    Again, I don't know what surface looks like but the area of the surface should be

    \int\int_{S_{xy}} \sqrt{1 + (\frac{\partial z}{\partial x})^{2} + (\frac{\partial z}{\partial y}})^{2}}dA.

    If I take the partials accordingly and plug them in I get

    \int \int_{S_{xy}} \sqrt{1 + x^{2} + y^{2}}}dA

    now I'm stuck.

    Any ideas?
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  2. #2
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    Spherical coordinates \displaystyle x^2+y^2=r^2. Then you can do trig sub \displaystyle 1+tan^2=sec^2
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  3. #3
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    Quote Originally Posted by dwsmith View Post
    Spherical coordinates \displaystyle x^2+y^2=r^2. Then you can do trig sub \displaystyle 1+tan^2=sec^2
    We haven't covered Spherical coordinates in our course yet, couldn't I obtain the some results with polar coordinates?
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  4. #4
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    How have you not covered spherical if you have done polar?
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