Question

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

67.5π2 mm
Start Fraction 67.5 pi over 2 End Fraction mm

5π18 mm
Start Fraction 5 pi over 18 End Fraction mm

15π mm
15 pi mm

18π mm
18 pi mm

Answer 1

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

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

where \( r \) is the radius and \( \theta \) is the central angle in radians.

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

Now substituting these values into the formula:

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

Calculating this step by step:

1. Multiply the radius by the angle:
\[
27 \times \frac{2\pi}{3} = \frac{27 \times 2\pi}{3} = \frac{54\pi}{3} = 18\pi \text{ mm}
\]

Thus, the length of the arc formed by the angle is \( 18\pi \) mm.

The correct answer is:

**18π mm**