Volume of Paraboloid-Bounded Solid in Cylindrical Coordinates?

[naspek]

Find the volume of the solid that lies under the paraboloid z = x^2 + y^2, above xy plane,
and inside the cylinder x^2 + y^2 = 2y

First, i try to find the range..
i transfer it to cylindrical coordinates..

sqrt(y^2)=<z<=r^2
i don't know how to find r
i know that phi is from 0 to 2pi because it's paraboloid right?
how am i going to eliminate y? because, y cannot exist in the cylindrical coordinate..

 

[lanedance]

the outer r limit will be the cylinder, the inner r limit the parabliod, express the inner limit as r(z)

the xy plane means the lower limit for z will be z=0

phi will be from 0 to 2pi, as there is nothing in the problem to limit the angular range, so you must integrate over the whole range

 

[lanedance]

don't forget the jacobian in the integral either

 

[naspek]

got it! thank u very much! =)