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So I am presented with the following problem:

Find the surface area of the cone $z=\sqrt{ x^2 + y^2} $ that lines inside the cylinder $x^2 + y^2 = 2x$.

Im pretty sure a double integral is involved, but I have no clue how to even go about starting this question... any ideas?

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    Your first surface isn't a cone...2012-08-15
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    @J.M., it seems to be a rather extended habit to call that thing a cone because it looks ridiculously close to a cone, at least for values of $\,x,y\,$ close to zero2012-08-15

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