Question 13
In Candlepin Bowling, ten cylindrical pins, each having a diameter of 3 inches, are arranged in a triangular layout, with the distance between the centres of the adjacent pins being 12 inches, as shown in the diagram below. If we use a rope having the shortest possible length to enclose the ten pins without moving them, as shown by the thick curve, the enclosed area is $a+b\sqrt3+\frac c4\pi$ square inches, where $a,b,c$ are integers. What is the value of $a+b+c$?
