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I've hit a roadblock on a question regarding Surface Integrals. I seem to be having a problem conceptualizing many of these concepts. Anyway, here goes.

*Find the area of the following surface using an explicit description of a surface.*

The cone \(z^2 = 4x^2 + 4y^2\) for \(0\leq z\leq4\)

I have solved for z and found the dS portion to = \(\sqrt{5}\) dA. This jives with the answer sheet that I have. It's the rest that I seem to be having troubles with.

Since it's a cone, shouldn't I just integrate like so?

\(\sqrt{5}\int_0^{2\pi}\int_0^4 (1)dz rdr \mbox{ for a final answer of }8\pi^2\sqrt5 \mbox{? The solution manual is showing an answer of }4\sqrt5\).

Any assistance, or a point in the right direction, will be greatly appreciated.

Thanks,

Mac