Question

Given a circle with a radius of 6, what is the length of an arc measuring 60°?

A.) 1/2pi
B.) 2pi
C.) 3/2pi
D.) 3pi

Answer 1

Answer:
`2\pi`

Explanation:

The length of arc with central angle x and radius r is given by ;-

`l=(x)/(360^(\circ))*2\pi r`

Given: The radius of circle = 6 units

Central angle = 60°

Now, the length of arc measuring 60° is given by :_

`l=(60)/(360^(\circ))*2\pi (6)\\\\\Rightarrow\ l=2\pi`

Hence, the the length of arc =
`2\pi`

Answer 2

First, determine the circumference of the circle by the equation, C = 2πr.
C = 2π(6) = 12π
Then, multiply this value by the ratio of the angle and whole revolution,
12π x (60° / 360°) = 2π
Thus, the length of the arc is 2π.