20060214, 21:36  #12  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2·7^{2}·109 Posts 
Quote:
If the question has a unique answer, and it phrased as if it must, the solution must be independent of the diameter of the sphere or the radius of the hole. In particular, the special case of a hole of zero radius and hence zero volume must yield the unique answer. This hole must clearly be drillled through a 6" diameter sphere. Paul 

20060215, 01:03  #13  
Bronze Medalist
Jan 2004
Mumbai,India
2^{2}·3^{3}·19 Posts 
Volume od a sphere
Quote:
Any sphere of diameter 6 inches and Above will yield a residue of 36 pi for a 6 inch long hole, including our earth! Fascinating isn't it? Mally 

20060215, 22:18  #14 
Aug 2003
Snicker, AL
959_{10} Posts 
Draw a square. It can be any size. Now draw a circle so that it fills the square. What is the relationship of the area of the circle to the area of the square?
Now draw the same square and put 4 identical circles inside it so they fill the square. What is the relationship of the area of the circle to the area of the square? Now draw the same square with 9 circles and figure the areas. What would it be with 16 circles? Hint, an easy approach to this is to use a square with sides 6 long. Use inches, cm, etc, whatever makes you happy. Fusion 
20060216, 04:41  #15  
Jun 2005
2×191 Posts 
Quote:
The way you described, the picture can still be reduced to smaller squares, so the ratios of areas are the same due to similarity. The only way to improve this is to change the packing. Hexagonal packing will be an improvement over the square packing you described. You can do even better if you allow circles of various sizes. Drew Last fiddled with by drew on 20060216 at 04:42 

20060216, 06:50  #16 
Aug 2003
Snicker, AL
7·137 Posts 
Its not a packing puzzle, its a relationship demonstration. You will see the relationship if you solve the elementary math involved. Leave the result in the form X(pi). You should also see the relationship to the above about a hole drilled into a sphere.
Fusion 
20060216, 14:17  #17  
Jun 2005
382_{10} Posts 
Quote:
Like I said. The ratio will always be the same due to similarity. It can always be divided into a number of circles inscribed in squares. Drew 

20060218, 20:46  #18 
Jun 2005
Near Beetlegeuse
184_{16} Posts 
Fusion,
When you say the circle "fills" the square, do you mean the sides of the square are tangent to the circle, or do you mean the circle touches the square at its corners? Thanks, 
20060219, 08:15  #19  
Bronze Medalist
Jan 2004
Mumbai,India
100000000100_{2} Posts 
Quote:
Mally 

20060220, 15:00  #20 
Aug 2003
Snicker, AL
1110111111_{2} Posts 
Inscribed in the square meets the conditions stated. However, a modified set of conditions would give a similar result for a circumscribed circle(s).
Fusion 
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