## Volume of region in space - triple integral

Consider the region bound by
$x^2 +y ^2 +z^2 = 4$ and the cone $z=-\sqrt(x^2+y^2)$ with $-\sqrt2\leqslant z\leqslant 0$

In spherical co-ords have i set up the correct bounds?

$\int_{0}^{(3\pi /4)}\int_{0}^{(2\pi)}\int _{0}^{\sqrt{2}} r^2\sin \theta drd\theta d\varphi$