Question

The area of a sector of a circle is given by the formula below. What is the solution for S?

Answer 1

So we have the formula for the area of a sector of a circle: $A= \pi r^2( \frac{s}{360} )$
where
$A$ is the area of the sector
$s$ is the central angle

To solve for $s$, we are going to divide both sides of the equation by $\pi r^2$, and then we are going to multiply both sides of the equation by 360°:
$A= \pi r^2( \frac{s}{360} )$ 
$\frac{A}{\pi r^2} = \frac{ \pi r^2( \frac{s}{360} )}{\pi r^2}$
$\frac{s}{360}= \frac{A}{\pi r^2}$
$\frac{s}{360}(360)= \frac{A}{\pi r^2} (360)$
$s= \frac{360A}{\pi r^2}$

We can conclude that the solution for s is: $s= \frac{360A}{\pi r^2}$