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Wrapping a Rope around the Earth Puzzle (TANTON Mathematics)

Suppose Poindexter takes a very long rope and wraps it around the equator of the Earth. Assume he has just the right length that makes this work without any slack. Suppose Allistair then comes along and adds 10 feet of rope to the length and the tiny bit of slack is used to have the rope uniformly hover just ever so slightly above the ground. How high off the ground is that rope? Let's answer this puzzle in one fell swoop for ALL planets, not matter their size, and answer it for cubical planets and triangular planets as well!
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