Question

Find the radius of the circle of the shaded sector has an area of 5pi and a central angle of 2pi/5 rads Please include steps !!!

Answer 1

5 units

Explanation:

Area of sector = ½ × r² × theta

5pi = ½ × r² × 2pi/5

r² = 5pi × 2 × 5/2pi

r² = 25

r = 5

Answer 2

r=5

Explanation:

The area of a sector is found by

A = 1/2 r^2 theta where theta is in radians

We know the area and we know theta

5pi = 1/2 r^2 (2 pi/5)

5pi = r^2 pi/5

Multiply each side by 5/pi to isolate r^2

5/pi * 5pi = r^2 pi/5 * 5/pi

25 = r^2

Take the square root of each side

sqrt(25) = sqrt(r^2)

5 =r