Question

Select the correct answer. A circle has a radius of 6 inches and a central angle of 60° what is the measure of the arc length associated with this angle? A. 6pi inches B. 3pi inches C. 2pi inches D. Pi inches

Answer 1

Given:

a.) A circle has a radius of 6 inches and a central angle of 60°

To be able to determine the measure of the arc length associated with the angle, we will be using the following formula:

$\text{ Arc Length = (}\frac{\theta}{360^{\circ}})2\pi r$

We get,

$\text{ Arc Length = (}\frac{\theta}{360^{\circ}})2\pi r$$\text{ = (}\frac{60^{\circ}}{360^{\circ}})2\pi(6)$$\text{ = (}\frac{1}{6})2\pi(6)\text{ = (}\frac{6}{6})(2\pi)$$\text{ Arc Length = 2}\pi$

Therefore, the measure of the arc length is 2pi. The answer is letter C.