How to calculate the volume of the solid described $x^2+ y^2+z^2 \le 9$ and $2 \le z \le \sqrt5$?

Question

How to calculate the volume of the solid described $x^2+ y^2+z^2 \le 9$ and $2 \le z \le \sqrt5$?

I try $x=2r \cos \phi$, $y=2r \sin \phi$, $z=z$, but but probably not the way to go

Answer 1

$$V=\int_{-2}^{2}\int_{-\sqrt{4-y^2}}^{\sqrt{4-y^2}}\int_{\sqrt{5}}^{\sqrt{9-x^2-y^2}}dzdxdy-\int_{-\sqrt{5}}^{\sqrt{5}}\int_{-\sqrt{5-y^2}}^{\sqrt{5-y^2}}\int_{2}^{\sqrt{9-x^2-y^2}}dzdxdy$$