I imagine 6 (six, SIX) poles, arranged and attached in this way that they form an equilateral triangle in section.


Then the rope has three lineare segments along each side of this equilateral triangle; 

each linear segment has the length equal to 4r = 4*3 = 12 inches.


Next, there are 3 arcs of 120 degrees each, contributing   =  to the rope length.


Having the rope wrapped two times around the circles bounded together, gives the length of such rope of


    2 * [ (3*4r) +  ] = 2*(3*4*3) +  = 72 + 4*3.14*3 = 109.68 inches (approximately.    ANSWER


Thus you have both the formula and the value.

    My arrangement of 6 poles is ONVIOUS:


        imagine first 3 poles lying next to each other on horizontal plane.

        imagine 2 poles in the next (second) row above the first one

        finally, imagine the last, third row over the two in the second row.

        Their centers form equilateral triangle, and this configuration is stable.


        Actually, this configuration is FIRST than come to the mind when speaking about it . . . 


        So, my solution is perfect, independently of what @greenestamps think or may think about it.