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 = (120)/(180)\pi = \frac23\pi ~rad`

We have r = 3 cm, then:

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