Hard to believe..

Here's an interesting problem. Suppose you take an extremely long ribbon and wrap it tightly around the Earth-along the equator, the distance being about 40000km. Imagine that the earth is smooth and that there no space whatsoever beneath the ribbon. Now suppose you lengthen the ribbon by 1meter. This would cause the ribbon to slack and will leave a gap from the surface of the earth to the ribbon. (look at the diagram)

How big is this gap? (Indicated by the arrow on the diagram)
Any guesses?
Well its roughly 16 centimeters. This is an interesting result many people find hard to believe. But a simple calculation will show you that it's true.
Here's the math,

For the initial case ,
c=pi*d
where
c- circumference of the earth and thus the initial length of the ribbon.
d- diameter of the earth
c1=c+1
c1-new length of the ribbon(after lengthening by 1 meter)
c1=pi*(d+2*x)
x- gap between earth and the ribbon(indicated by the arrow)
therefore,
pi*d+1=pi*d+2*pi*x
x=1/2*pi=0.159m
which is approximately equal to 16 centimeters.