#### Answer

$r^2=\dfrac{360A}{{\pi S}}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
S=\dfrac{360A}{\pi r^2}
$ for $
r^2
,$ use the properties of equality to isolate the variable.
$\bf{\text{Solution Details:}}$
Using the properties of equality to isolate the variable, the equation above is equivalent to
\begin{array}{l}\require{cancel}
S=\dfrac{360A}{\pi r^2}
\\\\
\pi r^2(S)=\pi r^2\left( \dfrac{360A}{\pi r^2} \right)
\\\\
\pi r^2S=360A
\\\\
\dfrac{\pi r^2S}{\pi S}=\dfrac{360A}{{\pi S}}
\\\\
r^2=\dfrac{360A}{{\pi S}}
.\end{array}