This one is actually an easy one, but perceptions can be deceiving. Before you do any setup for this problem, make a guess as to the answer then post both the guess and the answer. Be honest ;-)
Here is the problem:
I am going to make a couple of assumptions; first that the Earth is a smooth, perfect sphere; second, that the diameter is exactly 25000 miles. Here is the scenario:
There is a company that has a contract to build a fence all the way around the Earth at the equator. They get all of the stuff, then at the last minute, it is decided that the fence needs to be a foot off the ground in order that the twin headed purple tree snark can migrate back and forth across the equator. The question is how much more fencing material will the company have to purchase to raise the fence a foot off the ground?
If the fence is say scheduled to be four feet high from the ground, raising it a foot means that the fence, as originally planned was enough to cover that height as is. If the fence is one foot high from the ground, the top wire is already at the one foot height so flipping it is no big deal?
to guess, with my consternation about the previous quiz. But, since there is no stipulation in the question as to the height of the fence, I'll guess the answer is 0 feet additional. I'd just cut a foot off the bottom of the rolls of alleady purchased fencing and start installing.
senior moment, I'd probably cut off the top instead of the bottom of the rolls, and have to start all over :-). I've been sitting home all day with a chest cold, now you have my head hurting wore than my lungs.
An I know that the answer is much greater than you'd expect (or much less, can't really recall...)
Assuming that the circumference of the earth is 25000Xpi, a fence of 1' above the earth would create a circle 25002? (one foot all the way around on either end of a diameter). 25002xpi would be the new circumference.
the difference is 2pi...but I know that's wrong because it was too easy.
I've also seen it where the string around the earth needed to be lengthened so that a 6' tall man could walk under it at a single point... can't remember that one either...
My guess was 10~15% more. Started to work the problem and think I noticed a typo. The earth has, I know it, a circumference of about 25,000 miles. So... thought Dan was playing word games and I gave up the ship at that point(??). Thanks for the puzzle anyway, Dan.
It would be 25000 miles +2feet, not 25002 ;-) The answer is 2 π feet. The interesting thing is that it does not depend at all on the diameter of the sphere you are going around. The earth, the sun, or a basketball, to make it stand 1 foot above the sphere, it needs to be 2 π feet longer. Most people would tend to guess much higher.
Actually, just a slip, but it really doesn't matter. See my answer above. It is independent of the diameter of the sphere. to get it one foot higher, it needs to be 2 π feet longer.
