Question

Please help me with this question I am trying to help my son but I have forgotten how to solve these problems. The formula for the lateral surface area of a cylinder is S=2πrh, where r is the radius of the bases and h is the height.Solve for r.r=2hπ/Sr=h/2πSr=2Sπhr=S/2πh

Answer 1

We have the following formula:

$S=2\pi\text{ rh}$

and we need to isolate the radius r. Then, we can rewrite the formula as

$S=(2\pi h)\cdot r$

then, by dividing both side by 2Pi h, we have

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

since

$\frac{2\pi h}{2\pi h}=1$

we get

$\begin{gathered} \frac{S}{2\pi h}=1\cdot r \\ or\text{ equivalently} \\ \frac{S}{2\pi h}=r \end{gathered}$

By comparing this result with the given options, the answer is the last option:

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