There seems to be quite a lot of guessing going on in there.
Solve r^2 = 9 - r^2 to find the limits of 'r'.
You may wish to do 'z' first and have limits [ r^2 , 9 - r^2 ]
I am asked to find the volume between the two paraboloids z=9-x^2-y^2 and z=x^2 + y^2. Converting to cylindrical polar coordinates, these become z=9-r^2 and z=r^2. Clearly z ranges between 0 and 9 and I think r ranges from -sqrt(z) to + sqrt(z)? This given the integral which evaluates to 0! Have I made a mistake in my working?