Question

Given, $A=\frac{S}{360}\times \pi r^2$
$A$ is the area of setor, $S$ is the angle measure in degrees of the sector and $r$ is the radius of the circle. Find $r$ in terms of $A$ and $S$.

• A. $r=\frac{360A\pi }{S}$
• B. $r=\frac{360A}{S\pi }$
• C. $r=\sqrt{\frac{360A\pi }{S}}$
• D. $r=\sqrt{\frac{360A}{S\pi }}$

Answer 1

The correct option is D $r=\sqrt{\frac{360A}{S\pi }}$

To change the formula in terms of $A$ and $S$, Isolate $r^2$, we get the formula as
$\frac{A\times 360}{S\pi }=r^2$
Now taking square root on both the sides to get the value of $r$ in terms of $A$ and $S$.
$\therefore r=\sqrt{\frac{360A}{S\pi }}$