Question

Find the area of the shaded sector of the circle. Give the exact answer in terms of straight pi.

A circle has a central angle that measures 120 degrees and a radius of 8.


fraction numerator 48 straight pi over denominator 9 end fraction units squared

fraction numerator 64 straight pi over denominator 3 end fraction units squared

fraction numerator 32 straight pi over denominator 3 end fraction units squared

fraction numerator 16 straight pi over denominator 9 end fraction units squared

Answer 1

The area of the sector that has a central angle of 120 degrees and radius of 8 units is 64π / 3 units²

Area of a sector

The area of a sector is defined as follows:

area = ∅ / 360 × πr²

where

• r = radius
• ∅ = central angle

Therefore,

r = 8

∅ = 120°

Hence,

area of the sector = 120 / 360 × π × 8²

area of the sector = 1 / 3 × π × 64

area of the sector = 64π / 3 units²

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