Question

The formula gives the volume V of a right cylinder with radius r and height h.V = πr²hSolve for r

Answer 1

The formula that gives the volume V of a right cylinder with radius r and height h is presented below:

$V=\pi r^2h$

Step 1: Divide both sides by πh

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

Step 2: Take the square root of both sides.

$\begin{gathered} \sqrt[]{r^2}=\sqrt[]{\frac{V}{\pi h}} \\ r=\sqrt[]{\frac{V}{\pi h}} \end{gathered}$

Step 3: We can multiply both the numerator and denominator by πh to get:

$\begin{gathered} r=\sqrt[]{\frac{V\pi h}{\pi^2h^2}} \\ =\frac{\sqrt[]{V\pi h}}{\sqrt[]{\pi^2h^2}} \\ r=\frac{\sqrt[]{V\pi h}}{\pi h} \end{gathered}$

The correct option is the last one.