Question

If the length of an arc of measure 80° is 12pi inches, find the length of the radius of the circle.

Answer 1

27 inches

Explanation:

Circumference = π X D (D = diameter = 2 X radius)

Length of arc = (angle / 360) X circumference of circle

call radius r

circumference = 2πr

arc length = (80/360) X 2πr

12π = (80/360) X 2πr

2πr = (12π )/ (80/360)

= 54π.

so 2πr = 54π.

divide both sides by 2π:

r = 27 inches