Answer
$r=\pm\dfrac{\sqrt{A\pi}}{\pi}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of equality to solve the given equation, $
A=\pi r^2
,$ for $
r
.$
$\bf{\text{Solution Details:}}$
Dividing both sides by $
\pi
,$ results to
\begin{array}{l}\require{cancel}
\dfrac{A}{\pi}=r^2
\\\\
r^2=\dfrac{A}{\pi}
.\end{array}
Taking the square root of both sides (Square Root Principle) results to
\begin{array}{l}\require{cancel}
r=\pm\sqrt{\dfrac{A}{\pi}}
.\end{array}
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{A}{\pi}\cdot\dfrac{\pi}{\pi}}
\\\\
r=\pm\sqrt{\dfrac{A\pi}{\pi^2}}
\\\\
r=\pm\sqrt{\dfrac{1}{\pi^2}\cdot A\pi}
\\\\
r=\pm\sqrt{\left( \dfrac{1}{\pi}\right)^2\cdot A\pi}
\\\\
r=\pm\dfrac{1}{\pi}\sqrt{A\pi}
\\\\
r=\pm\dfrac{\sqrt{A\pi}}{\pi}
.\end{array}