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

18π mm
18 pi mm

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

15π mm

Answer 1

To find the length of the arc formed by a central angle in a circle, you can use the formula for the arc length \( L \):

\[
L = r \theta
\]

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

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

Now, substitute the values into the formula:

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

Now, perform the multiplication:

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

Simplify:

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

Thus, the length of the arc is

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