I love polar coordinates, but not very familiar with them...

Here is the problem:

Use polar coordinates to find the volume of the given solid.

Below the paraboloid z = 36 - 9x^2 - 9y^2 and above the xy-plane.

My attempt:

the paraboloid can be rewritten as x^2+y^2 = 4

in this case, i thought the limits in polar coordinates would be:

0 <= theta <= pi

0 <= r <= 2

since the radius of the circle is 2 and is only in the first two quadrants.

since r = x^2 + y^2.... it is just the double integral of r^2 dr d-theta. in that case i got my final answer to be 8/3(pi).

Where did I get my reasoning wrong? Thanks