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The groove around the moon (Posted on 2002-05-06) Difficulty: 3 of 5
Imagine you would have to put a rope around the moon. Since the moon is 1,738,000 metres in diameter, this is a hard task. Finally you have managed to get the rope around the moon but... it is one meter short.

You decide to dig a groove all around the moon, so that the shorter rope suffices. How deep must this groove be? (Assume the Moon to be a perfect sphere.)

  Submitted by charl    
Rating: 2.9167 (12 votes)
Solution: (Hide)
The outline of a circle is always 2 * Pi * R (R = the radius). Therefore, the radius will have to decrease by: 100 centimetres / (2 * Pi) = 100 / 6,28 = R = 15,92 cm.

So, to put the cable tightly around the moon the groove should be 15,92 centimetres deep. Which is still a huge task if you want to gid this deep all around the moon.

The fun thing is, that the depth of the groove does not depend on the radius of the object you are digging it in.

You could as well 'dig a groove' in the globe on your desk: it would still have to be 15,92 centimetres.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionA different (and simple) approachJayDeeKay2015-06-05 18:08:30
re(2): answerK Sengupta2008-06-07 16:32:10
re: answerDej Mar2008-06-07 12:38:51
answerK Sengupta2007-05-15 04:19:42
re: Zero Option Solutionowl2004-10-28 12:42:37
SolutionZero Option SolutionCeeAnne2004-10-27 15:28:24
Differencesbob9092004-10-27 09:44:21
re: dig itprashant2004-03-29 07:52:16
dig itprashant2004-03-29 07:39:08
SolutionSolutionAntonio2003-08-24 03:16:48
No SubjectLucifer2003-03-01 09:12:26
SolutionNo Subjectdanny2002-11-12 17:42:33
You winMike2002-07-24 22:53:55
re: Got to be wrong!TomM2002-07-24 07:34:23
Got to be wrong!Mike2002-07-24 05:25:51
My AnswerTom2002-05-09 12:47:14
thanksJohn Ryder2002-05-09 08:04:52
Well...levik2002-05-08 20:22:10
I understand what you're saying...butJohn Ryder2002-05-08 13:08:49
Look at it this waylevik2002-05-08 11:34:48
I don't understand the SolutionJohn Ryder2002-05-08 07:11:38
SolutionStuff N. Things2002-05-07 17:55:53
ring around the WHAT?Dan Dise2002-05-07 13:45:41
But....John2002-05-07 12:28:11
solution?John Ryder2002-05-07 11:45:39
But only...John2002-05-07 10:43:32
Interesting observationWhiskey Pete2002-05-07 09:29:50
Hmmm...Tim2002-05-07 08:59:17
SolutionTerry2002-05-07 08:58:34
David Rowley Correcttoferc2002-05-07 07:37:16
Solution?David Rowley2002-05-07 07:17:42
1 meter??kevin2002-05-07 07:07:13
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