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

56.5 mm
56.5 mm

47.1 mm
47.1 mm

0.9 mm
0.9 mm

106.0 mm

Answer 1

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

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

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

In this case:
- \( r = 27 \) millimeters,
- \( \theta = \frac{2\pi}{3} \) radians.

Now, plug in the values into the formula:

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

Calculating it step by step:

1. First calculate \( 27 \times \frac{2}{3} \):

\[
\frac{2}{3} \times 27 = 18
\]

2. Now multiply by \( \pi \):

\[
18\pi \approx 18 \times 3.14159 \approx 56.54867 \text{ mm}
\]

Rounding it to one decimal place gives \( 56.5 \text{ mm} \).

Thus, the length of the arc is approximately **56.5 mm**.