Band around the Earth - Solution

The Puzzle: The circumference of the Earth is approximately 40,000 kilometres, and someone has just made a metal band that circles the Earth, touching the ground at all locations. You come along at night, as a practical joke, and add just 10 metres to its length (one hundredth of one kilometer !) It is now one four-millionth longer, and sits magically just above the ground at all locations How far has it risen ... could a flea, a rabbit or even a man squeeze underneath it? Use the formula Circumference = 2 × pi × Radius Before: Original Circumference = 2 × pi × R After: Original Circumference + 10 = 2 × pi × (R + Gap) Subtracting the two: 10 = 2 × pi × Gap So, the Gap = 10 / (2 × pi) = 1.6m So a man could fit under it easily (though he might bump his head)