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

Answer:

84.78

Step-by-step 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°:

$\dfrac{120^o}{360^o}=\dfrac{1}{3}$

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

Therefore:

$A_S=\dfrac{1}{3}\cdot81\pi=27\pi$

Use π ≈ 3.14

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