Eiffel Tower.

[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

[xilman]

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

[mfgoode]

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

[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)

[xilman]

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

[mfgoode]

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