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## Homework Statement

Find the surface area of the part of the cone z = sqrt[(x^2 + y^2)] lying inside the cylinder x^2 - 2x + y^2 = 0.

**2. The attempt at a solution**

Partial Derivative x = x/sqrt(x^2 + y^2)

Partial Derivative y = y/sqrt(x^2 + y^2)

so...

sqrt((Partial Derivative Y) ^2 + (Partial Derivative at Y) ^ 2 + 1) =

sqrt[(x^2 + y^2)/(x^2 + y^2) + 1] = sqrt[2]

so...

the surface area =

integral on E of sqrt[2] r dr d(theta),

where E is the region (r, theta)|(0 < r < 2, 0 < theta < pi)

My books solution has the body of the integral as 5, and E as (0<r<1, 0<theta<pi)

I'm pretty sure I've just made an algebraical mistake in the body, but for the limits I'm confused. I don't know how to treat a cylinder that isn't centered at the origin. I thought r was always the distance from the origin... is it really the distance from the center of the cylinder?

Thanks for any help or advice you can give me.