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 15π mm 15 pi mm 5π18 mm Start Fraction 5 pi over 18 End Fraction mm 18π mm 18 pi mm 67.5π2 mm

1 answer

The length of an arc can be calculated using the formula:

Length of arc = (central angle / 360) x 2πr

Given that the central angle is 2π/3 and the radius is 27 mm, we plug these values into the formula:

Length of arc = (2π/3 / 360) x 2π x 27
Length of arc = (1/3) x 2π x 27
Length of arc = 2π x 9
Length of arc = 18π mm

Therefore, the length of the arc formed by a central angle of 2π/3 in a circle with a radius of 27 mm is 18π mm.