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

Answer:

$\frac{\pi }{10}$

Step-by-step 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 × $\frac{x}{2\pi }$ ← substitute values

5π = π × 10² × $\frac{x}{2\pi }$

5π = 100π × $\frac{x}{2\pi }$ (cancel 50π and 2π )

5π = 50x ( divide both sides by 50 )

x = $\frac{5\pi }{50}$ = $\frac{\pi }{10}$ ← central angle