Question

A circle has a sector with area 33 pi and central angle of 11/6 pi radians. What is the area of the circle?

Answer 1

Explanation:

Area of the sector =

[pi*r^2*11*pi/6]/360=pi^2*r^2*11/6*360=pi*r^2*11*180/2160=33 pi

r^2=71280/11*pi=6480/pi=6480/180=36

Area of the circle=pi*r^2=36 pi

Answer 2

The area of the circle is
`36\pi\ units^(2)`

Explanation:

we know that

The area of a circle subtends a central angle of
`2\pi` radians

so

By proportion find the area of the circle

`(33\pi )/((11\pi /6))=(x)/(2\pi)\\ \\ x=2\pi*( 33*6)/11\\ \\x=36\pi\ units^(2)`