Cut the Rope\text{Cut the Rope}

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Imagine a rope that runs completely around the Earth's equator flat against the ground. You cut the rope and tie in another piece of rope that is 710710 inches long. That will increase the total length of the rope by a bit more than the length of a bus.

A sphere with circumference 710 inches

Now imagine that the rope is lifted at all points simultaneously, so that it floats above the Earth at the same height all along its length. What is the largest thing that could fit underneath the rope?

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