Question

A circle with area 81ㅠ has a sector with a central angle of 120°.

What is the area of the sector?

Either enter an exact answer in terms ofㅠ or use 3.14 forㅠ and enter your answer as a decimal.

Answer 1

84.78

Explanation:

We have the area of a circle

`A_O=81\pi`

The sector with a central angle of

`120^o`

Calculate, what part of 360° is an angle 120°:

`(120^o)/(360^o)=(1)/(3)`

The same part of an area of a circle is an area of a segment.

Therefore:

`A_S=(1)/(3)\cdot81\pi=27\pi`

Use π ≈ 3.14

`A_S\approx(27)(3.14)=84.78`