Question

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

67.5
π
2
mm
67 point 5 pi over 2 mm

15
π
mm
15pi mm

18
π
mm
18pi mm

5
π
18
mm

Answer 1

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

\[
L = r \theta
\]

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

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

Now, plug in the values into the formula:

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

Calculating this gives:

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

So, the length of the arc is:

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