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

Answer:

Option B $2\pi\ units$

Step-by-step 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°

$\frac{12\pi}{360}=\frac{x}{60}\\ \\x=12\pi(60)/360\\\\x=2\pi\ units$