Question

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 5π18 mm 5 pi over 18 mm 18π mm 18pi mm 67.5π2 mm 67 point 5 pi over 2 mm 15π mm

Answer 1

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

\[
L = r \theta
\]

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

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

Now we can substitute the values into the formula:

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

Calculating this:

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

Thus, the length of the arc is:

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