(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

g(x,y,z) = z^{2}; Ʃ is the part of the cone z = [itex]\sqrt{x^{2}+y^{2}}[/itex] between the planes z = 1 and z = 3.

2. Relevant equations

Conversion to polar coordinates

∫∫_{Ʃ}g(x,y,z)dS = ∫∫_{R}g(x,y,f(x,y)) [itex]\sqrt{f_{x}^{2}+ f_{y}^{2}+1}[/itex]

3. The attempt at a solution

If we're talking in terms of r and θ, r goes from 1 to 3 and θ goes from 0 to 2π. I converted to polar coordinates from cartesian and I got 8*π*√2 *z^{2}. If you were converting to polar/cylindrical coordinates, z^{2}wouldn't change, correct?

Sorry, for some reason the square root LaTeX command didn't want to work...

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# Surface integral of a cone

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