math fun

Band around the Earth - SolutionPuzzles -> Measuring Puzzles
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 locationsHow far has it risen ... could a flea, a rabbit or even a man squeeze underneath it?
. . . . (Scroll down if you really want to see the Solution ...) . . . . . .
The Solution . . .
Use the formula Circumference = 2 × pi × RadiusBefore: Original Circumference = 2 × pi × RAfter: Original Circumference + 10 = 2 × pi × (R + Gap)Subtracting the two:10 = 2 × pi × GapSo, the Gap = 10 / (2 × pi) = 1.6mSo a man could fit under it easily (though he might bump his head)