Find the Center of Mass of a Solid Find the Center of Mass of a Solid of constant density $\rho$ bounded below by the disk $R: x^2 + y^2 \leq 4$ in the plane $z=0$ and above by the paraboloid $z = 4 - x^2 - y^2.$ 
(Hint: By symmetry, $\overline{x} = \overline{y} = 0,$ so you only have to compute $\overline{z}$.)
Can anyone help me set up this integral? I am having trouble figuring out where to start with this problem. Thanks

First calculate the volume of the solid using polar coordinates
$$V = \iint_{x^2+y^2 \le 4} \int_{z = 0}^{4-x^2-y^2} dzdxdy = \iint_{x^2+y^2 \le 4} (4-x^2-y^2)\,dxdy = 2\pi \int_{r=0}^2 r(4-r^2)\,dr = 8\pi$$
Then we have
\begin{align}
z_{\text{cm}} &= \frac1V\iint_{x^2+y^2 \le 4} \int_{z = 0}^{4-x^2-y^2} z\,dzdxdy \\
&= \frac1{2V} \iint_{x^2+y^2 \le 4} (4-x^2-y^2)^2\,dxdy\\
&= \frac\pi{V}  \int_{r=0}^2 r(4-r^2)^2\,dr\\
&= \frac18 \cdot \frac{32}3\\
&= \frac43
\end{align}
