Question

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

Answer 1

Answer:

$10\pi\ cm$ or $31.4\ cm$

Step-by-step 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

$\frac{30\pi}{360^o}=\frac{x}{120^o}\\\\x=30\pi(120^o)/360^o\\\\x= 10\pi\ cm$

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