The length of an arc of a circle can be calculated using the formula:
Arc Length = (θ/360) * 2πr
Where:
- θ is the central angle of the arc in degrees.
- r is the radius of the circle.
Given that the central angle θ is 60 degrees and the radius r is 2r, we can substitute these values into the formula:
Arc Length = (60/360) * 2π(2r)
Simplify:
Arc Length = (1/6) * 2π(2r)
Arc Length = (1/6) * 4πr
Arc Length = (2/3)πr
So, the length of the 60 degree arc on a circle with radius 2r is (2/3)πr.
