I'm studying for my calculus exam and having difficulty with this question.

Find the volume lying between the paraboloids

and

.

I know to switch to polar coordinates, so

and

. The solution to the question says that they intersect where

, which I understand is just because you're setting z=z and solving, and that r can also be subbed in to be

. But then the solution says they intersect at that equation where z=z, "i.e. on the cylinder

. Is this just solving for

from the

?

I suppose my question is, what is the process I follow to solve this question? The solution integrates over the disc of radius 1, sets the intersection equation to zero with everything on one side, and integrates. But I don't know why.

The final answer is

cubic units.

Thanks so much for your help.