The central angle that captures the brown arc is 120°. To find out what fraction of the total circumference the brown arc is, we can find the ratio of this 120° angle to the total central angle of a circle, which is 360°. So we have:
Now we know the brown arc is
of the total circumference. The circumference is π*diameter, so in this case it’s 24π.
Finally, we do:
Now we know the brown arc is
Finally, we do: