Question

If a circle has a central angle of 2π/3 and a radius of 27 mm, how long is the arc formed by that angle?(1 point)
Responses
15π mm

5π/18 mm

67.5π/2 mm

18π 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 of the circle,
- \( \theta \) is the central angle in radians.

In this case:
- The radius \( r = 27 \) mm
- The central angle \( \theta = \frac{2\pi}{3} \) radians

Plugging in these values:

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

Calculating this:

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

Therefore, the length of the arc is \( \boxed{18\pi \text{ mm}} \).