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( (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( (s)/(360) )`

`(A)/(\pi r^2) = ( \pi r^2( (s)/(360) ))/(\pi r^2)`

`(s)/(360)= (A)/(\pi r^2)`

`(s)/(360)(360)= (A)/(\pi r^2) (360)`

`s= (360A)/(\pi r^2)`

We can conclude that the solution for s is:
`s= (360A)/(\pi r^2)`