Question

If a circle has a central angle of 2π3
and a radius of 27 millimeters, how long is the arc formed by that angle?(1 point)
Responses

5π18
mm
5 pi over 18 mm

18π
mm
18 pi mm

15π
mm

Answer 1

To find the length of the arc formed by a central angle in a circle, you can use the formula:

\[
\text{Arc Length} = r \cdot \theta
\]

where \( r \) is the radius and \( \theta \) is the central angle in radians.

Given:
- Radius \( r = 27 \) mm
- Central angle \( \theta = \frac{2\pi}{3} \) radians

Now, substitute the values into the formula:

\[
\text{Arc Length} = 27 \cdot \frac{2\pi}{3}
\]

Calculating this step-by-step:

\[
\text{Arc Length} = 27 \cdot \frac{2\pi}{3} = \frac{54\pi}{3} = 18\pi
\]

So, the length of the arc is \( 18\pi \) mm.

Thus, the correct response is:

**18π mm**