Answer
The required value is $h=\frac{22}{\pi {{r}^{2}}}$ and the expression in terms of $r$ is $2\pi {{r}^{2}}+\frac{44}{r}$.
Work Step by Step
Consider the equation $\pi {{r}^{2}}h=22$. Solve for $h$.
Divide both sides $\pi {{r}^{2}}$,
$\begin{align}
& \pi {{r}^{2}}h=22 \\
& \frac{\pi {{r}^{2}}h}{\pi {{r}^{2}}}=\frac{22}{\pi {{r}^{2}}} \\
& h=\frac{22}{\pi {{r}^{2}}}
\end{align}$
Therefore, the required value $h=\frac{22}{\pi {{r}^{2}}}$.
Now, re-write the expression $2\pi {{r}^{2}}+2\pi rh$ in terms of $r$.
Substitute $h=\frac{22}{\pi {{r}^{2}}}$,
$\begin{align}
& 2\pi {{r}^{2}}+2\pi rh=2\pi {{r}^{2}}+2\pi r\left( \frac{22}{\pi {{r}^{2}}} \right) \\
& =2\pi {{r}^{2}}+2\left( \frac{22}{r} \right) \\
& =2\pi {{r}^{2}}+\frac{44}{r}
\end{align}$
Therefore, the expression in terms of $r$ is $2\pi {{r}^{2}}+\frac{44}{r}$.
