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## Homework Statement

Use cylindrical coordinates to find (a) the volume and (b) the centroid of the solid S bounded above by the plane z=y and below by the paraboloid z=x

^{2}+y

^{2}.

## Homework Equations

V= ∫∫∫dv

x= r cos θ, y=sin θ, z=z

## The Attempt at a Solution

For the first integral I got that the limits are from r

^{2}to r sin θ, then I integrated with respect to z, but after that I don't know where "r" begins and ends how do I find the interval?