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

15π
mm
15 pi mm

18π
mm
18 pi mm

5π18
mm

Answer 1

To find the length of the 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 millimeters, and the central angle \( \theta \) is \( \frac{2\pi}{3} \) radians.

Now, plug in the values:

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

Now perform the multiplication:

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

So, the length of the arc formed by that angle is:

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

Thus, the correct response is **18π mm**.