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

18π mm
18 pi mm

67.5π2 mm
Start Fraction 67.5 pi over 2 End Fraction mm

15π mm
15 pi mm

5π18 mm
Start Fraction 5 pi over 18 End Fraction 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 and \( \theta \) is the central angle in radians.

Given:

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

Substituting these values into the arc length formula:

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

Calculating:

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

Thus, the length of the arc is:

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