That sounds right. Don't forget the Jacobian determinant though.
I have one small doubt in one of the question and would appreciate your advise.
I have this question to find the volume of cone \phi =\pi /4 by the sphere \rho =2 a cos\phi .
I think that:
1. I need to use triple integrals
2. \phi goes from 0 to \pi /4, \rho goes from 0 to 2 a cos\phi and \theta goes from 0 to 2\pi .
Am I on the right track?