Question

A circle has a radius of 12.6 cm.

Answer 1

Circle circumference = 12.6 cm * 2 * PI
Circle circumference = 25.2 cm * PI
a 120 degree arc would be (1/3) of the circumference
120 degree arc = (25.2 / 3) cm * PI
120 degree arc = 8.4 PI centimeters

Answer 2

Answer:

Length of an arc is given by:

$l = r \theta$

where,

r is the radius of the circle

$\theta$ is the angle in radian.

As per the statement:

A circle has a radius of 12.6 cm.

⇒r = 12.6 cm

It is also given that: a central angle measuring 120°.

Use conversion:

1 degree = $\frac{\pi}{180}$

then;

120 degree  =$120 \cdot \frac{\pi}{180} = \frac{\pi}{1.5}$

⇒$\theta = \frac{\pi}{1.5}$

then;

$l = r \theta$

Substitute the given values we have;

$l = 12.6 \cdot \frac{\pi}{1.5} = 8.4 \pi$ cm

therefore, the  exact length of an arc is, $8.4 \pi$ cm