Solution
= Solution
The projection onto the $x$-$y$ <plane> is the <disk> $x^2+y^2\leq4$. In <polar coordinates>, the height is $4-r^2$ and the <polar area element> is $r\,dr\,d\theta$. The <volume> is therefore
$$
\boxed{\mathcal V=\int_0^{2\pi}\int_0^2(4-r^2)r\,dr\,d\theta
=2\pi\left[2r^2-\frac{r^4}{4}\right]_0^2=8\pi}.
$$
The radial factor here is required because this <integral> is being constructed from the geometric <volume>, unlike the already specified <integral> in (a).