Question

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

15π
mm
15pi mm

67.5π2
mm
67 point 5 pi over 2 mm

18π
mm
18pi mm

5π18
mm
5 pi over 18 mm

Answer 1

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

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

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

In this case, the radius \( r \) is 27 mm and the central angle \( \theta \) is \(\frac{2\pi}{3}\).

Now, substituting these values into the formula:

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

Calculating that:

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

So the length of the arc is:

**18π mm**