A sector of a circle has a central angle of 100. If the area of the sector is 250\pi, what is the radius of the circle?
+9466 area of sector / area of circle = 100 / 360
Let r be the radius of the circle so the area of the circle = π r2
Substitute 250π in for the area of the sector and substitute π r2 in for the area of the circle.
250π / (π r2) = 100 / 360
Cancel out the π's in the first fraction
250 / r2 = 100 / 360
Flip both sides of the equation
r2 / 250 = 360 / 100
Multiply both sides of the equation by 250
r2 = 360 / 100 * 250
Simplify the right side of the equation.
r2 = 900
Take the positive square root of both sides.
r = 30
