Chapter 2.1, Problem 41PPSE

Solution

Solve the volume of a cylinder $V=\pi r^{2}h$ for h .

  $h=\frac{V}{\pi r^2}$ .

  $\left(C\right)$ is the correct option.

Given:

  $V=\pi r^{2}h$ .

The given options are

  $\begin{array}{l}\left(A\right)\frac{r^2}{\pi V}\left(B\right)\frac{\pi V}{r^2}\\ \left(C\right)\frac{V}{\pi r^2}\left(D\right)\frac{\pi r^2}{V}\end{array}$

Calculation:

It has been given that $V=\pi r^{2}h$ .

Divide both sides by $\pi r^2$

  $\begin{array}{c}\frac{V}{\pi r^2}=\frac{\pi r^{2}h}{\pi r^2}\\ \frac{V}{\pi r^2}=h\\ h=\frac{V}{\pi r^2}\end{array}$

Hence, $\left(C\right)$ is the correct option.