Question

Select the correct answer.

a circle has a radius of 6 inches and central angle of 60°. what is the measure of the arc length associated with this angle?
3pi
2pi
pi
6pi inches

Answer 1

`2\pi` inches

Option B

Explanation:

The arc length is proportional to the central angle
If L is the arc length and θ is the central angle in degrees

`L = (\theta)/(360) * C`

where C is the circumference of the circle

Given radius r = 6 inches, C = 2πr = 2π·6 = 12π
θ = 60°

So

`L = (60)/(360) * 12\pi\\\\= (1)/(6) * 12\pi\\\\= 2\pi\;inches`