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?

18 π mm

15 π mm

5 π/18 mm

67.5 π/2 mm

Answer 1

To find the length of the arc formed by the central angle, we can use the formula for arc length:

\[
L = r \theta
\]

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

Given:
- \( r = 27 \) mm,
- \( \theta = \frac{2\pi}{3} \).

We can substitute these values into the formula:

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

Calculating this gives:

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

Thus, the length of the arc is:

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