Question

A circle has a sector with area 27 and central angle of 120

What is the area of the circle?
Either enter an exact answer in terms of
or use 3.14 for it and enter your answer as a decimal.

Answer 1

81π

Explanation:

-The sum of central angles in a circle add up to 360°.

-Let x be the area of the circle.

-Given the area of a 120° is 27π, the circles area can be calculated as:

`A=27\pi\\\\120\textdegree=27\pi\\360\textdegree=x\\\\\therefore x=(360\textdegree* 27\pi)/(120\textdegree)\\\\=3* 27\pi\\\\=81\pi`

Hence, the area of the circle is 81π