Question

A sector with an area of 26pi cm^2 has a radius of 6cm. What is the central angle measure of the sector in radians?

A: 13pi/9
B: 9pi/13
C: 13pi/18
D: 18pi/13

Answer 1

A

Explanation:

Answer 2

A

Explanation:

The area (A ) of the sector is calculated as

A = area of circle × fraction of circle

= πr² ×
`(x)/(2\pi )` ( x is the measure of the central angle ) , thus

π × 6² ×
`(x)/(2\pi )` = 26π

36π ×
`(x)/(2\pi )` = 26π (cancel 36π and 2π )

18x = 26π ( divide both sides by 18 )

x =
`(26\pi )/(18)` =
`(13\pi )/(9)` → A