Question

If a sector in a circle of radius 10 has an area of 5pi, what is the measure of the central angle that forms the sector?

Answer 1

`(\pi )/(10)`

Explanation:

The area (A) of the sector is calculated using the formula

A = area of circle × fraction of circle

let x be the measure of the central angle, then

A = πr² ×
`(x)/(2\pi )` ← substitute values

5π = π × 10² ×
`(x)/(2\pi )`

5π = 100π ×
`(x)/(2\pi )` (cancel 50π and 2π )

5π = 50x ( divide both sides by 50 )

x =
`(5\pi )/(50)` =
`(\pi )/(10)` ← central angle