Question

The measure of the arc of a sector is 72 degrees, and the area of the sector is 5π in². What is the radius of the circle?

A. 5 inches
B. 10 inches
C. 15 inches
D. 20 inches

Answer 1

The radius of the circle is 5 inches.

Step-by-step explanation:

To find the radius of the circle, we can use the formula for the area of a sector: A = πr2. Given that the area of the sector is 5π in² and the measure of the arc is 72 degrees, we can set up the following equation:

5π = πr2 * (72/360)

Simplifying the equation, we get 5 = r2 * (72/360)

Dividing both sides by (72/360), we get r2 = 5 / (72/360) = 5 / (1/5) = 5 * 5 = 25

Taking the square root of both sides, we find that the radius of the circle is r = 5 inches.