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Conference dypss1::brain_bogglers

Title:Brain Bogglers
Notice:BRAIN_BOGGLERS is, like, back in business, totally
Moderator:BUSY::SLAB
Created:Mon Jul 13 1987
Last Modified:Mon Jun 02 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:1441
Total number of notes:13981

1441.0. "belt around the earth" by 4446::OSMAN (Eric Osman, dtn 226-7122) Tue May 27 1997 14:56

If this was discussed in here, it's been awhile, so I resurrect:


A belt is drawn tight around the equator of the (assume spherical) Earth.

We now add 12 inches to the belt, and distribute the slack evenly.

The slack belt will be:

A)	Seemingly still tight, since 12" compared with the size of the
	Earth is unnoticable

B)	Several inches above the Earth all the way around


This is not a trick question.  Please show your work.

/Eric

T.RTitleUserPersonal
Name
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1441.1CSC32::MACGREGORColorado: the TRUE mid-westTue May 27 1997 15:176
    
    I don't know if it is posted in here anywhere, but I remember
    discussing this once before verbally.  I'd love to show the work, but
    I'm missing the radius of the earth.
    
    Marc
1441.2BUSY::SLABAudiophiles do it 'til it hertz!Tue May 27 1997 15:554
    
    	Doesn't really matter, but round it off to a 25K-mile circumference,
    	or a 3979-mile radius.
    
1441.3BUSY::SLABAudiophiles do it 'til it hertz!Tue May 27 1997 15:573
    
    	BTW, note 82 sort of touches on this problem.
    
1441.4How about 2"39702::BERGARTJeff-the-refTue May 27 1997 16:1024
IMHO, you do not need to know the radius of the earth.
(Using C for circum. of the earth, and D for its Diameter)

	C = Pie * D
	
	Now solve for the new diameter:

	C + 12" = Pie * (D + delta).  Using the distributed law;

	C + 12" = (Pie * D) + (Pie * delta)

	The C and (Pie * D) terms can be crossed out since they are equal!

	leaving:

	12" = Pie * delta

	Using 22/7 for Pie, one gets:

	(12"/22)*7 = delta  or

	delta = approx. 3.8" therefore, the change to the radius is half that
	 	or approx. 1.9"