Question

A circle has a sector with area 27\pi27π27, pi and central angle of \purple{120^\circ}120 ∘ start color #9d38bd, 120, degrees, end color #9d38bd. What is the area of the circle?

Answer 1

The answer: 81π

Answer 2

The radius of the circle is 9 units.

Explanation:

To calculate the area of the circle we need to find it's radius, since we have the area of the sector and it's angle, therefore we can calculate the radius by using the following formula:

sector area = (central angle)*pi*r²/360

27pi = 120*pi*r²/360

27pi = pi*r²/3

27 = r²/3

r² = 81

r = sqrt(81) = 9

The radius of the circle is 9 units.