In a circle, a 90degrees sector has area 144pi in2. What is the radius of the circle?

Question

asked May 2, 2021 19.0k views

1 Answer

Ethan Mick · Answer 1 · 2021-05-07T13:55:17+0000

Answer:

The radius of the circle is 24 inches.

Explanation:

Central angle in a sector is 90 degrees

Area of a sector is
$144\pi\ \text{inch}^2$

The area of sector is given by the formula as follows :

$A=(\theta)/(360)\pi r^2$

r is the radius of circle

$r=\sqrt{(360 A)/(\theta \pi)} \\\\r=\sqrt{(360 * 144\pi )/(90* \pi)} \\\\r=24\ \text{inch}$

So, the radius of the circle is 24 inches.