The area of a sector

Question

The area of a sector of a circle with a diameter 0f 8 cm is 16π/3 square cm. Find the measure of the central angle of the sector.

Answer 1

Let θ = radian measure of the sector's central angle

 

Area of sector = (1/2)(radius)²θ

 

                16π/3 = (1/2)(4)²θ

 

                16π/3 = 8θ     So, θ = 2π/3 = 120°