Question

If a circle has a central angle of 2 pie over 3 and a radius of 27 millimeters, how long is the arc formed by that angle? (1 point)

• 15т mm

57 mm
18

67.5 mm

• 18 mm

Answer 1

To find the length of the arc formed by a central angle in a circle, the formula is:

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

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

In this case, the radius \( r = 27 \) mm and the central angle \( \theta = \frac{2\pi}{3} \) radians.

Now plug in the values:

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

Calculating this:

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

Now, to approximate \( 18\pi \):

Using \( \pi \approx 3.14 \):

\[
18\pi \approx 18 \times 3.14 \approx 56.52 \text{ mm}
\]

So, the actual length of the arc is around 57 mm.

Therefore, the correct answer is **57 mm**.