Question

If $A=\pi (R^2-r^2)$, then $R$ is equal to

• A. $\sqrt{\frac{A-\pi r^2}{\pi }}$
• B. $\sqrt{\frac{A+\pi r^2}{\pi }}$
• C. $\sqrt{\frac{r^2\pi -A}{\pi }}$
• D. $\sqrt{\frac{r^2\pi -A}{r}}$

Answer 1

The correct option is B $\sqrt{\frac{A+\pi r^2}{\pi }}$

Given, $A=\pi (R^2-r^2)$

Therefore, $A=$ $\pi R^2-\pi r^2$

$\Rightarrow A+\pi r^2=\pi R^2$
$\Rightarrow R^2=\frac{A+\pi r^2}{\pi }$
$\Rightarrow$ $R=\sqrt{\frac{A+\pi r^2}{\pi }}$