Hello, the question asks me to find the volume of the region above $\displaystyle z=\sqrt{x^2+y^2}$ and $\displaystyle x^2+y^2+z^2=2az$.

I get to the integral $\displaystyle \int^{2\pi}_0 \int^{\frac{\pi}{2}}_{\frac{\pi}{4}} \int^{2a}_0 \rho^2 \sin \phi d \rho d \phi d \theta$ but I get the wrong answer (answers say it is $\displaystyle \pi a^3$.

What is wrong with my integral?

Thanks

EDIT: I think I know the mistake I made. I now end up with the integral $\displaystyle \int^{2\pi}_0 \int^{\frac{\pi}{2}}_{\frac{\pi}{4}} \int^{2a \cos \phi}_0 \rho^2 \sin \phi d \rho d \phi d \theta$ but I still get the wrong answer... I get $\displaystyle \frac{\pi a^3}{3}$... are the answers wrong, or...?

EDIT 2: I've solved this problem... I don't need any more help on this. Thanks