A sector of a circle has a central angle of 80 degrees. If the area of the sector is 32pi, what is the radius of the circle?

AdminMod2
Aug 18, 2017

#1**0 **

80 / 360 = 2/9

Area of circle = Pi x Radius^2

32Pi = 2/9 * Pi * r^2

Solve for r:

32 π = (2 π r^2)/9

32 π = (2 π r^2)/9 is equivalent to (2 π r^2)/9 = 32 π:

(2 π r^2)/9 = 32 π

Divide both sides by (2 π)/9:

r^2 = 144

Take the square root of both sides:

Answer: | r = 12 units

Guest Aug 18, 2017

edited by
Guest
Aug 18, 2017