24K Pipe & the Banana Slug

Here is an interesting little puzzle. It isn't so much a puzzle as a highly counter-intuitive reality. If you run the math to check your assumptions, you might think you've been hit by the Intel Processor computation bug. :-)

To help you out, the average radius of the Earth is about 3,959 miles, and the classic formula is: "circumference = 2 \* pi \* radius", where "pi" is approximately 3.14156. Polar (3,949.8 mi) and Equatorial (3,963.2 mi) radii are close enough to assume a perfect (smooth) sphere for this problem.

Your company has just completed a massive global engineering project. You've built a particle
accelerator, a superconducting supercollider that circumnavigates the globe! A perfectly circular hollow pipe thru which protons and anti-protons are accelerated and smash into each other.

But just before you flip the switch to energize the superconducting magnets, the UN caves to the protest of environmentalists. Seems your pipe is hindering the migration of the
revered Banana Slug in the forests adjacent to Santa Cruz (apparently there are a lot of laywers there with nothing better to do, except maybe sue IBM). You are commanded to raise the level of the pipe by 3 feet. Since the shape must remain a perfect circle, you must raise the pipe by this much around the entire length of the 24,850 mile pipe, not just there in Santa Cruz.

Try to guess the length of the segment of pipe you will need to add to raise the level of the supercollider by 3 feet around the entire circumference of the globe (multiple choice). After you've made a guess, go ahead and run the math.

  1. More than 5,000 feet
  2. 1,000-2,000 feet
  3. 100-200 feet
  4. Less than 20 feet

Extra credit: What if you wanted to "raise" by 3 feet a circular pipe with a radius equal to the distance between the Sun and Neptune (average radius = 2,798,842,261 miles)?

In case you give up, here is the solution:
http://blogs.sun.com/roller/resources/dcb/SOLUTION_24K_Pipe.html

Comments:

Wouldn't "raising" any pipe by 3 feet (regardless if it was originally 20 feet or 200M feet) just increase it by PI \* 3 feet = ~ 9.5 feet?

Posted by Bill Hathaway on February 28, 2005 at 09:00 AM EST #

Well, 2 \* PI \* 3 feet (C = 2\*pi\*R), so it would be about 19ft or so (I think you forgot the 2). But it seems, according to the math, you would always need 19ft to raise any circumference 3 ft, no matter the radius: C = 2\*pi\*R, so if R is 3 more than it was before, C1 = 2\*pi\*(R+3), which you can distribute to C1 = 2\*pi\*R + 2\*pi\*3. 2\*pi\*3 is about 19ft no matter the original radius. Weird! :)

Posted by Keith on February 28, 2005 at 03:35 PM EST #

Very good Keith (and Bill). Yes, it is weird. The math is simple. The result is non-intuitive.

Posted by Dave Brillhart on March 01, 2005 at 03:08 AM EST #

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