Hi, I have to compute de volume for the region:

I've tried to do by two different parametrizations, in spherics and cylindrical coordinates

For cylindrical coordinates I've made:

For spherics I've considered

I've used wolfram to make the calculus, and it gives that for cylindrical coord. I'm having twice the volume that I have for spherical coord. I don't know where I'm committing the mistake. Bye, thanks for helping :)

Note: I'm multiplying by 3 because I was going to use for Gauss theorem and is the divergence for the vector field given by the problem