Answer
$r=\pm\dfrac{\sqrt{3V\pi h}}{\pi h}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To solve the given equation, $
V=\dfrac{1}{3}\pi r^2h
,$ in terms of $
r
,$ use the properties of equality and the Square Root Principle to isolate the variable.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
3(V)=\left(\dfrac{1}{3}\pi r^2h\right)3
\\\\
3V=\pi r^2h
\\\\
\dfrac{3V}{\pi h}=r^2
\\\\
r^2=\dfrac{3V}{\pi h}
.\end{array}
Taking the square root of both sides (Square Root Principle), the equation above is equivalent to
\begin{array}{l}\require{cancel}
r=\pm\sqrt{\dfrac{3V}{\pi h}}
.\end{array}
Rationalizing the denominator by multiplying the radicand by an expression equal to $1$ which will make the denominator a perfect power of the index results to
\begin{array}{l}\require{cancel}
r=\pm\sqrt{\dfrac{3V}{\pi h}\cdot\dfrac{\pi h}{\pi h}}
\\\\
r=\pm\sqrt{\dfrac{3V\pi h}{\left(\pi h\right)^2}}
\\\\
r=\pm\sqrt{\dfrac{1}{\left(\pi h\right)^2}\cdot3V\pi h}
\\\\
r=\pm\sqrt{\left(\dfrac{1}{\pi h}\right)^2\cdot3V\pi h}
\\\\
r=\pm\dfrac{1}{\pi h}\sqrt{3V\pi h}
\\\\
r=\pm\dfrac{\sqrt{3V\pi h}}{\pi h}
.\end{array}
