Solve the triple integral $\iiint_D (x^2 + y^2 + z^2)\, dxdydz$ How does one go about solving the integral: 
$$
\iiint_D (x^2 + y^2 + z^2)\, dxdydz, 
$$
where 
$$
D=\{(x,y,z) \in \mathbb{R}^3: x^2 + y^2 + z^2 \le 9\}. 
$$
I believe I am supposed to convert to spherical coordinates but I would need some help with how this is done and what the answer to this integral would be.
Thanks in advance!

$$
\int_{0}^{3}{\rm d}r\,r^{2}\times r^{2}\quad
\overbrace{\int{\rm d}\Omega_{\,\vec{r}}}^{4\pi}\
=\
4\pi\,{3^{5} \over 5}
=
{972 \over 5}\,\pi
$$
