The complete circumference of each of those circles with radius 3,
is given by
C = 2pr = 2p(3) = 6p
So the sum of all three circumferences is 3 times that or
18p
However, from that, we must subtract the three arcs that are inside the
green equilateral triangle that are shown below:
Since that is an equilateral triangle, each angle is 60°.
Since 60° is 1/6th of 360°, each arc is 1/6th of a circumference,
so we must subtract 1/6 of the total of the three circumferences,
which will leave 5/6 of the 18p we
calculated.
So the answer is 15p.
Edwin
