Answer
$\frac{81 \pi}{10}.$
Work Step by Step
The volume of revolution is given by
$$
\pi \int_{0}^{3}\left(3 x-x^{2}\right)^{2} d x=\pi \int_{0}^{3}\left(x^{4}-6 x^{3}+9 x^{2}\right) d x\\=\left.\pi\left(\frac{1}{5} x^{5}-\frac{3}{2} x^{4}+3 x^{3}\right)\right|_{0} ^{3}=\frac{81 \pi}{10}.
$$
