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January 11, 2015

Band around the Earth Puzzle

The circumference of the Earth is approximately 40,000 kilometers, 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 meters 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?

7 comments:

Shivraj Gawde said...

yes..definitely..
anything lesser than 1.6 meters..

dogtag114 said...

Not even a flea...

c = 2 pi r^2
r ^2 = c / (2 pi)
r = SQRT( c/(2 pi))
2521.4046 r in meters
2521.4049 r in meters (+10m)

JyRKS said...
This comment has been removed by the author.
Anonymous said...

Should be fairly simple calculation. Isn't C = pi x D ? 40,000,000 meters is a diameter of 12,732,395.447 meters and 40,000,010 meters diameter would be a diameter 12,732,398.630 meters. The difference (3.2m) divided by 2 would be 1.6m. The kid who answered first looks to be correct.

Ray Taff said...

JyRKS, I think your decimal is in the wrong place. 10 meters is 1/100th of a kilometer, not 1/1000th. LOL. The kid was right in the first answer. 40,000,000 / 3.14159265359 = 12,732395.45 METERS and 40,000,010 / 3.14159265359 = 12,732398.63. The difference in diameter (3.18m) / 2 = 1.59meters above the surface of the earth.

Ray Taff said...

JyRKS, I think your decimal is in the wrong place. 10 meters is 1/100th of a kilometer, not 1/1000th. LOL. The kid was right in the first answer. 40,000,000 / 3.14159265359 = 12,732395.45 METERS and 40,000,010 / 3.14159265359 = 12,732398.63. The difference in diameter (3.18m) / 2 = 1.59meters above the surface of the earth.

Thomas Riley said...

Since the circumference formula is 2(pi)(r), adding 10 meters to the circumference would thus add

10=2(pi)(r)
divide by 2
5=(pi)(r)
r=5/pi

5/pi meters to the radius, which is about 1.6 meters to the radius.

Everyone root for the first guy! I just did the proof (if you can call it that).