Question

Which represents r in terms of A and S?

Answer 1

Answer:

$r=\frac{6\sqrt{10AS}}{S\sqrt{\pi }}$

Step-by-step explanation:

Given the formula;

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

We want to solve the given formula for r.

Multiply both sides by $\frac{360}{\pi S}$

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

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

Take square root of both sides

$r=\sqrt{\frac{360A}{\pi S}}$

$r=\frac{\sqrt{360A}}{\sqrt{\pi S}}$

$r=\frac{\sqrt{360A}}{\sqrt{\pi }\sqrt{S}}$

$r=\frac{\sqrt{360A}\times \sqrt{S}}{\sqrt{\pi }\sqrt{S} \times \sqrt{S}}$

$r=\frac{\sqrt{360AS}}{S\sqrt{\pi }}$

$r=\frac{6\sqrt{10AS}}{S\sqrt{\pi }}$