Question

A circle has a circumference of 18 cm. What is the length of an arc that has a measure of 160°?

Answer 1

Answer:

$8\:\mathrm{cm}$

Step-by-step explanation:

By definition, the length arc is a portion of a circle's circumference. The exact amount is directly proportional to the measure of the arc. Therefore, the formula for the length of an arc with measure (in degrees) $\theta$ is $2\pi r\cdot \frac{\theta}{360}$, where $2\pi r$ is the circumference of the circle.

Substituting $2\pi r=18$ and $\theta=160^{\circ}$:

$L_{arc}=18\cdot \frac{160}{360}=\boxed{8\:\mathrm{cm}}$