The circumference of a circle is 16π cm. What is the area of a sector whose central angle measures 120°?

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The circumference of a circle is 2πr, where r is the radius of the circle, so the radius of this circle is 16π ⁄ 2π = 8 cm. The area of a circle is equal to πr 2 , so the area of this circle is (8) 2 π = 64π cm 2 . The area of a sector is equal to the area of the circle multiplied by the fraction of the circle that the sector covers. That fraction is equal to 120 ⁄ 360 , so the area of the sector is equal to 120 ⁄ 360 (64π) = 1 ⁄ 3 (64π) = 64 ⁄ 3 π cm 2 .

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