Step $2$

The region $D$ is the region inside the curve of intersection of the paraboloid with the $xy-$plane, $S$ radius $33,$ and so we know that for $D$ we have $0r3$

$$ and $0$

Step $3$

Now the volume is found by the integral

$V={\displaystyle \underset{0}{\overset{2}{}}}{\displaystyle \underset{0}{\overset{3}{}}}(27-3r^2)rdrd={\displaystyle \underset{0}{\overset{2}{}}}{\displaystyle \underset{0}{\overset{3}{}}}(27r-3r^3)drd$

The inner integral is

${\displaystyle \underset{0}{\overset{3}{}}}(27r-3r^3)dr=[\frac{27}{2}{r}^2-{]}_0^3=$

$$

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