Answer
$(A) r=\frac{\sqrt{A\pi}}{\pi} $.
Work Step by Step
Area of the circle:
$\Rightarrow A=\pi r^2$
Divide both sides by $\pi$.
$\Rightarrow \frac{A}{\pi}=\frac{\pi r^2}{\pi}$
Simplify.
$\Rightarrow \frac{A}{\pi}= r^2$
Divide and multiply the left hand side by $\pi$:
$\Rightarrow \frac{A\pi}{\pi^2}= r^2$
Take the square root of both sides:
$\Rightarrow \sqrt{\frac{A\pi}{\pi^2}}= \sqrt{r^2}$
Simplify.
$\Rightarrow \frac{\sqrt{A\pi}}{\pi}=r$
Hence, the correct option is $(A) r=\frac{\sqrt{A\pi}}{\pi} $.
