Question

Given a circle with a radius of 6, what is the length of an arc measuring 60°? A. 1 2 p B. 2p C. 3 2 p D. 3p

Answer 1

Option B
`2\pi\ units`

Explanation:

step 1

Find the circumference of the circle

The circumference is equal to

`C=2\pi r`

we have

`r=6\ units`

substitute

`C=2\pi (6)`

`C=12\pi\ units`

step 2

Find the length of an arc measuring 60°

we know that

The circumference of the circle subtends a central angle of 360 degrees

so

using proportion

find the length of an arc measuring 60°

`(12\pi)/(360)=(x)/(60)\\ \\x=12\pi(60)/360\\\\x=2\pi\ units`