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Puzzle Corner. The Solution to The Band Around the Earth
In the last issue of MTN we asked you to see if you could work out what would happen if you added just 10 metres to a tight fitting steel band that was wrapped tightly around the earth. Congratulations if you sent in the correct answer.
Assume that the circumference of the earth is 40,000 kilometres and the steel band fits so tightly that you can't even slide a piece of paper underneath it. What effect would the addition of 10 metres have to the gap between the earth and the steel band? Would a piece of paper slip underneath? A mouse maybe, or would a man now be able to get through the gap?
Here is 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!