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  1. c=2pi(r), 2pi=6.283, c=6.283r. New circumference comes from adding 1 unit (in this case a foot) to the radius. So now we have c_2=2pi(r+1), 2pi=6.283, 6.283(r+1)=6.283r+6.283. The difference from the new circumference and the previous one is 6.283 units, this works for every case. This is EXACTLY why you would need 6.283 more units of rope added to your circumference (feet specifically).

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