Answer:
[tex]r=\frac{6\sqrt{10AS}}{S\sqrt{\pi }}[/tex]
Step-by-step explanation:
Given the formula;
[tex]A=\frac{\pi r^2S}{360}[/tex]
We want to solve the given formula for r.
Multiply both sides by [tex]\frac{360}{\pi S}[/tex]
[tex]A\times \frac{360}{\pi S}=\frac{\pi r^2S}{360} \times \frac{360}{\pi S}[/tex]
[tex]A\times \frac{360}{\pi S}=r^2[/tex]
Take square root of both sides
[tex]r=\sqrt{\frac{360A}{\pi S}}[/tex]
[tex]r=\frac{\sqrt{360A}}{\sqrt{\pi S}}[/tex]
[tex]r=\frac{\sqrt{360A}}{\sqrt{\pi }\sqrt{S}}[/tex]
[tex]r=\frac{\sqrt{360A}\times \sqrt{S}}{\sqrt{\pi }\sqrt{S} \times \sqrt{S}}[/tex]
[tex]r=\frac{\sqrt{360AS}}{S\sqrt{\pi }}[/tex]
[tex]r=\frac{6\sqrt{10AS}}{S\sqrt{\pi }}[/tex]
