Okay, let's solve this step-by-step:
* The central angle measures (2pi)/3 radians
* Converting to degrees: (2pi)/3 radians = (2*3.14)/3 = 120 degrees
* The radius of the circle is 6 cm
To find the length of an arc intercepted by an angle (in degrees) and radius, we use the formula:
Arc Length = (Degrees * pi * Radius) / 180
So in this case:
Arc Length = (120 * 3.14 * 6) / 180 = 36 cm
Therefore, the length of the arc intercepted by the central angle is 36 cm.
Let me know if you have any other questions!