Volume under paraboloid and over a disk
Ok its a simple question really... say that I have to find the volume (using polar coordinates) of the solid under the paraboloid z=x^2+y^2 and above the disk x^2+y^2≤9. My approach would be to find the z value of where the cylinder and paraboloid intersect. Then find the volume of the paraboloid using the value of the plane where it intersects, then subtract it from the volume of the cylinder, this seems right to me. I'm getting z=18 for the point where the cylinder and paraboloid intercept, is this right? For some reason my gut is telling me that its 9 not 18. I simply plugged in the radius of the circle into the paraboloid formula. is there another way that I am missing?