Question

For a circle with a radius of 15 cm, what is the length of an arc intercepted by an angle measuring 120°?

A)
51 cm
870 cm
107 cm
127 cm

Answer 1

Explanation:

About 31.4 based on the other answers I have seen.

Answer 2

`10\pi\ cm` or
`31.4\ cm`

Explanation:

step 1

Find the circumference of the circle

The circumference of a circle is equal to

`C=2\pi r`

we have

`r=15\ cm`

substitute

`C=2\pi (15)`

`C=30\pi\ cm`

step 2

Remember that the circumference of the circle subtends a central angle of 360 degrees

so

using proportion

Find the length of an arc by a central angle of 120 degrees

`(30\pi)/(360^o)=(x)/(120^o)\\\\x=30\pi(120^o)/360^o\\\\x= 10\pi\ cm`

The exact value of the length of the arc is
`10\pi\ cm`

assume

`\pi=3.14`

`10(3.14)=31.4\ cm` ---> approximate value