Find the volume inside the sphere and outside the cylinder .

My attempt : I visualized the volume I must calculate. I can first calculate the volume of the sphere ( ) and then calculate the volume of the cylinder inside the sphere. This is where I'm having problems.

I think its volume is the following one, but I'm unsure : ...

(I've used cylindrical coordinates for the volume of the cylinder inside the sphere, a better said, the part of the cylinder.)

I'd like to know if what I did until now is right. If so I'd have to remember how to solve the iterated integral I got.