Question

The arc length of a circle intercepted by a central angle of 41.9° is 9.9 inches, what is the radius of the circle? Round to the nearest 10th of an inch.

Answer 1

Radius = 13.8 inches

Explanation:

The relationship between arc length, s , the radius r and central angle θ in radians is given by the formula

s = rθ where r = radius, θ is central angle in radians

Or,

r = s/θ

Given s = 9.9 in and θ = 41.4° we get

θ in radians = (θ in degrees) x π/180 radians

So 41° = 41 x π/180 radians = 0.7156 radians

r = s/θ

r = 9.9/0.7156

r = 13.835 inches

Rounded to the nearest tenth:

r = 13.8 inches