Finding the volume using cylindrical coordinates

[Ki-nana18]

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=x²+y².

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 r² 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?

 

[Ki-nana18]

May I have some help on this?