To find the length of the arc given the central angle, multiply (the fraction of the angle of the full circle, 360°, that the central angle, 120°, makes up)*(the total circumference of the circle). You're basically finding the fraction of the circumference that is covered by the central angle, if that makes any sense.
So the central angle makes up [tex] \frac{120\°}{360\°} = \frac{1}{3}[/tex] the entire circle. You are given that the circumference of the circle is 18. Multiply the fraction of the full circle that the central angle makes up ([tex] \frac{1}{3}[/tex]) by the circumference of the circle:
[tex]\frac{1}{3} \times 18 = 6[/tex]
The length of your arc is 6.
Let me know if you're confused b/c my explanation isn't the greatest :) I'll try to explain it better if you don't understand.
