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Eiffel tower - science puzzle


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The Eiffel tower in Paris has including the tv antenna an height of 321 meter. It is made out of 7 million kg steel. Somebody would like to build a scale model of this tower with a weight of 1 kg. How tall will this scale model be? Eiffel tower


Let's call the reduction factor of the scale model x. Hence all lengths in the scale model are x times as small as in the original Eiffel tower. Therefore the volume of the scale model is x*x*x = x^3 times as small as the original volume.
The mass of an object is equal to its volume times the density of the material it is made of. The ratio between the mass of the Eiffel tower and the scale model is 7,000,000 : 1. Hence the volume of the Eiffel tower is 7,000,000 times as that of the scale model. That implies that all length scales in the Eiffel tower are (7,000,000)^(1/3) = 191.29 times as large as in the scale model. Hence since the Eiffel tower has a height 321 meter, the 1 kg scale model should have an height of 321/191.29 = 1.68 meter.