## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$r^2=\dfrac{360A}{{\pi S}}$
$\bf{\text{Solution Outline:}}$ 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}