Question

In circle P, if the radius is 3 cm, what is the length of arc AD?

Answer 1

Hello there.

We have for a circle that:

$\ell=\alpha r$

Where:

$\ell$ is the measure of the arc

$\alpha$ is the measure of the angle (radians)

$r$ is the radius of the circle

In our case, we have $\alpha = 120^\circ = \dfrac{120}{180}\pi = \frac23\pi ~rad$

We have r = 3 cm, then:

$\ell = (\frac23\pi )(3\ cm)\\ \\ \boxed{\ell = 2\pi~cm}$