#### Answer

$r=\pm\dfrac{\sqrt{S\pi}}{2\pi}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
S=4\pi r^2
,$ 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}
\dfrac{S}{4\pi}=r^2
\\\\
r^2=\dfrac{S}{4\pi}
.\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{S}{4\pi}}
.\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{S}{4\pi}\cdot\dfrac{\pi}{\pi}}
\\\\
r=\pm\sqrt{\dfrac{S\pi}{4\pi^2}}
\\\\
r=\pm\sqrt{\dfrac{1}{4\pi^2}\cdot S\pi}
\\\\
r=\pm\sqrt{\left(\dfrac{1}{2\pi}\right)^2\cdot S\pi}
\\\\
r=\pm\dfrac{1}{2\pi}\sqrt{S\pi}
\\\\
r=\pm\dfrac{\sqrt{S\pi}}{2\pi}
.\end{array}