# If the circumference of a circle is 12, and the angle measure of an arc is 60°, what is the length of the arc?

Jun 2, 2018

the length of the arc is 2

#### Explanation:

As a circle is ${360}^{o}$ and ${60}^{o}$ is $\frac{1}{6}$ of that, the length of the arc will also be $\frac{1}{6}$ of the full circle, i.e. $\frac{12}{6} = 2$

Jun 2, 2018

Length of arc= $\theta \times \frac{\pi}{180} \times r$
Circumference=$2 \pi r$

$12 = 2 \pi r$
$\frac{12}{2} = \pi r$

$6 = \pi r$

$6 = \frac{22 r}{7}$

$6 \times 7 = 22 r$

$42 = 22 r$

$\frac{42}{22} = r$

$r = \frac{21}{11} c m$

Length of arc$= 60 \times \frac{\frac{22}{7}}{180} \times \frac{21}{11}$

Length of arc$= 60 \times \frac{22}{7 \times 180} \times \frac{21}{11}$

Length of arc$= \cancel{60} \times \frac{\cancel{22}}{\cancel{1260}} \times \frac{21}{\cancel{11}}$

Length of arc$= 1 \times \frac{2}{\cancel{21}} \times \frac{\cancel{21}}{1}$

Length of arc= 2cm