# Computing the volume when one figure is intersected with another

How can I compute the volume of $$x^2 + y^2 + z^2 = 4$$ when it is cut with $$x^2 + y^2 = 2y$$?

The first one is a sphere and the second one is a cylinder. The general formula is

$$\int_{0}^{2\pi}\int_{0}^{\rho}\int_{0}^{h}r\mathop{dz}\mathop{dr}\mathop{d\theta}$$

I've drawn a picture but I still cannot get the bounds correct. Can someone help me?

EDIT: You can write $$2y + z^2 = 4$$, and plugging in $$z = 0$$, I believe a maximum occurs at $$y = 2$$