Volume of cylinder:

\(

\begin{align}

&= \pi r^2h \\

&= \pi \cdot 3^2 \cdot 20 \\

&= \pi \cdot 9 \cdot 20 \\

&= 180\pi \, \text{cm}^3

\end{align}

\)

Volume of hemisphere:

\(

\begin{align}

&= \frac{2}{3}\pi r^3 \\

&= \frac{2}{3} \cdot \pi \cdot 3^2 \\

&= 2 \cdot \pi \cdot 3^2 \\

&= 2 \cdot \pi \cdot 9 \\

&= 18\pi

\end{align}

\)

Volume of the solid:

\(

\begin{align}

&= 180\pi \times 18\pi \\

&= 198\pi \, \text{cm}^3

\end{align}

\)