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)

Question

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.