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19. Imagine...

Imagine a piece of string stretching for 25000 miles right round the equator and tied so that it just touches the (perfectly spherical, of course) surface of the Earth. OK, OK.....but just imagine...

Now cut the string and add an extra length of one metre, retie and put it back round the Equator so that there's now a small gap between the string and the surface of the Earth.

Assume, naturally, that this gap is the same all the way round. How big is it?


 

Scroll down the page for the answer.


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

The diagram shows the Earth (inner circle) and, greatly exaggerated, the string (outer circle).

So if C1 is the circumference of the outer circle and C2 is the circumference of the inner circle then

C1 = 2 * pi * (r + h)

and

C2 = 2 * pi * r

Remember, we've added an extra metre of string so the difference between the two circumferences is just that, and so

C1 - C2 = 1

so

2 * pi * (r + h) - 2 * pi * r = 1

so

2 * pi * h = 1

so

h = 1 / 2pi

and, since the '1' is actually 1 metre, then this means that h is roughly 16 cm or just over six inches - a result that surprises many!
 

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