I have a problem that I've been stuck on for a while as follows,(adsbygoogle = window.adsbygoogle || []).push({});

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!

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# Homework Help: Surface area of intersecting cylinder and sphere

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