If a circle has a central angle of 2π3 and a radius of 27 millimeters, how long is the arc formed by that angle?

Answer 1

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

Arc length = (central angle / 360) x 2πr

where r is the radius of the circle.
Given that the central angle is 2π/3 and the radius is 27mm, plug these values into the formula:

Arc length = (2π/3 / 360) x 2π x 27
Arc length = (2/3 x 2π/360) x 2π x 27
Arc length = (2/3 x 1/180) x 2π x 27
Arc length = 2/540 x 54π
Arc length = 2/5 x 3π
Arc length = 6π/5

Therefore, the length of the arc formed by a central angle of 2π/3 in a circle with a radius of 27 millimeters is 6π/5 millimeters.