Hey guys. I'm stuck on a problem for my calc class.

Let D be the region bounded by the paraboloids and . Find the volume of the region D using an iterated integral.

I have been trying all night to come up with the limits of integration and the general set up, and I am at a loss.

So far I have tried to solve by subbing z for itself:

but this does not leave a clean answer to transform into spherical.

you're left with:

, and I can't see any way to get this into a nice format.

We have a test coming up and my professor said a problem like this would be on it. Any help would be greatly appreciated.