Question

The formula for the lateral surface area of a cylinder is $\mathrm{S}=2\mathrm{\pi rh}$ , where $r$ is the radius of the bases and $h$ is the height.

Solve for $h$.

• A. $h=\frac{r}{2S\pi }$
• B. $h=2S\pi r$
• C. $h=\frac{S}{2\pi r}$
• D. $h=\frac{Sr}{2\mathrm{\pi }}$

Answer 1

The correct option is C

$h=\frac{S}{2\pi r}$

Explanation for correct option:

The formula for the lateral surface area of a cylinder is $\mathrm{S}=2\mathrm{\pi rh}$.

Isolate $h$ to one side of equation.

$\begin{array}{rcl}\frac{S}{2\mathrm{\pi r}}& =& h\\ \therefore h& =& \frac{S}{2\mathrm{\pi r}}\end{array}$

Hence, option $C$ is correct.

Explanation for the incorrect answer:

The obtained expression is $h=\frac{S}{2\mathrm{\pi r}}$

It is not equal to $h=\frac{r}{2S\pi }$.

The option $A$ is not correct.

The obtained expression is $h=\frac{S}{2\mathrm{\pi r}}$.

It is not equal to $h=2S\pi r$.

The option $B$ is not correct.

The obtained expression is $h=\frac{S}{2\mathrm{\pi r}}$.

It is not equal to $h=\frac{Sr}{2\mathrm{\pi }}$.

The option $D$ is not correct.

Therefore, option $C$ is correct.