Question

A circle has a sector with area 27 pi and a central angle of 120 degrees. what’s the area of the circle?

Answer 1

`81\pi`

Explanation:

This may appear problem of geometry but can be simply solved using concept of ratio.

Since circle is uniform figure , hence area is uniformly distributed over the circle. Hence , area will be equally distributed for each angle of circle.

Given

sector with 120 degree angle has area
`27\pi`

to get area covered by unit angle we divide both angle and area by 120

sector 120/120 degree angle has area
`27\pi /120`

sector with 1 degree has area
`27\pi /120`

We know that total angle for a circle is 360 degree.

Hence, area for circle will be 360 times multiplied the area of sector with 1 degree has area
`27\pi /120` of same circle

Thus area of circle =
`=>360*(27\pi /120)\\=> 3*27\pi \\=> 81\pi`