Question

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

67.5π/2 mm
5π/18 mm
15π 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 for arc length:

\[
L = r \cdot \theta
\]

where:
- \(L\) is the arc length,
- \(r\) is the radius, and
- \(\theta\) is the central angle in radians.

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

Substituting the values into the formula:

\[
L = 27 \cdot \frac{2\pi}{3}
\]

Calculating this gives:

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

Therefore, the length of the arc is:

\[
\boxed{18\pi} \, \text{mm}
\]