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?
.
.
.
.
.
.
.
.
(Scroll down if you really want
to see the Solution ...)
.
.
.
.
.
.
The Solution . . .
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)
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?
.
.
.
.
.
.
.
.
(Scroll down if you really want
to see the Solution ...)
.
.
.
.
.
.
The Solution . . .
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)
