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Homework Help: Surface area of intersecting cylinder and sphere

  1. Jul 30, 2008 #1
    I have a problem that I've been stuck on for a while as follows,

    Find the surface area of the part of the cylinder [tex]x^{2}+y^{2}=2ay[/tex] in the first octant that lies inside the sphere [tex]x^{2}+y^{2}+z^{2}=4a^{2}[/tex]. Express your answer in terms of a single integral in [tex]\phi[/tex], you do not need to evaluate this integral.

    I've started by parametrization the cylinder as [tex]S(\theta,z)=(\sqrt{2ay}cos(\theta),(\sqrt{2ay}sin(\theta),z)[/tex]. I then went on take the derivative of S in terms of [tex]\theta[/tex] and z and took the cross product of the terms. I know the bounds of integration for [tex]\theta[/tex] should be 0 to Pi/2, but from there I'm unsure of what to do in terms of setting up the bounds for z.

    Any help would be appreciated, thanks!
  2. jcsd
  3. Jul 30, 2008 #2


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    Homework Helper

    That looks more like an ellipse than a circle in the x-y plane. There is a special parametrisation for ellipses, but you have to express the equation in the form of an ellipse first. Secondly, your parametrisation for [tex]S(\theta,z)[/tex] is incorrect. It is supposed to consist only of [tex]\theta,z[/tex] and other constants. It shouldn't have y as a variable.
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