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 2006-02-03, 16:26 #1 mfgoode Bronze Medalist     Jan 2004 Mumbai,India 1000000001002 Posts Eiffel Tower. Here is one I pinched from India's super human computer who beat a UNIVAC 1108 at its own game -number crunching. She is Shakuntala Devi whom I have had the good fortune to have met on 3 occasions! A smaller replica of the Eiffel Tower is to be made in the same metal as the tower i.e. Iron/Steel. These are the particulars: It is 300 metres high The total weight is 8,000.000 Kg Same material to be used, only 1 Kg. How high do you make the height of the scaled down model? Mally
2006-02-03, 21:03   #2
xilman
Bamboozled!

"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across

2×3×29×67 Posts

Quote:
 Originally Posted by mfgoode Here is one I pinched from India's super human computer who beat a UNIVAC 1108 at its own game -number crunching. She is Shakuntala Devi whom I have had the good fortune to have met on 3 occasions! A smaller replica of the Eiffel Tower is to be made in the same metal as the tower i.e. Iron/Steel. These are the particulars: It is 300 metres high The total weight is 8,000.000 Kg Same material to be used, only 1 Kg. How high do you make the height of the scaled down model? Mally
The mass scales as the volume, which scales as the cube
of the linear dimension.

So the linear dimension of the model must be (1/8000000)^{-3}, or 1/200.

Therefore the model must be 300/200m high, or 1.5m.

Paul

 2006-02-07, 07:31 #3 mfgoode Bronze Medalist     Jan 2004 Mumbai,India 40048 Posts Eiffel Tower You hit the nail on the head Paul. Excellent deduction. Many people don't know of this property of similar volumes and it was my intention to high light it in this problem. Mally
 2006-02-07, 11:46 #4 tom11784     Aug 2003 Upstate NY, USA 2×163 Posts Two technicalities 1) The problem statement mixing notation 8,000.000kg read to me as 8,000kg instead of 8,000,000kg 2) The scale factor is (1/8,000,000)^(1/3), not (1/8,000,000)^(-3)
2006-02-07, 12:56   #5
xilman
Bamboozled!

"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across

101101100010102 Posts

Quote:
 Originally Posted by tom11784 Two technicalities 1) The problem statement mixing notation 8,000.000kg read to me as 8,000kg instead of 8,000,000kg 2) The scale factor is (1/8,000,000)^(1/3), not (1/8,000,000)^(-3)
You are entirely correct on the second point. It was a silly typo on my part.

Paul

2006-02-07, 14:53   #6
mfgoode
Bronze Medalist

Jan 2004
Mumbai,India

22×33×19 Posts
Eiffel Tower.l

Quote:
 Originally Posted by tom11784 Two technicalities 1) The problem statement mixing notation 8,000.000kg read to me as 8,000kg instead of 8,000,000kg 2) The scale factor is (1/8,000,000)^(1/3), not (1/8,000,000)^(-3)
:surprised Good observation tom 11784.
In the 1st point its easier to spot the cube root in my notation. For that matter a large quantity like that could be expressed as 8 kilo tonnes (metric).
Mally

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