>>The shape is irrelevant.
>>
>>You have to think in 3 dimensions.
>>
>>In this case if you reduce the height from 300 m to 30 cm (1/1000) you also have to reduce the width and lenght (z axis) to the same proportions.
>>
>>8000 tons / 1000 / 1000 / 1000 = 8 grams
>>
>>HTH :)
>
>I know it's irrelevant. But I still want to know how it is calculated. Not for this particular puzzle, but in general.

If you have 2 objects, that are exactly proportional in shape but different sizes, then their volumes vary as the cube of any linear dimension. As a simple example, take a cube. A cube 10 units on a side has 1000 times the volume of a cube 1 unit on a side: (10 / 1) ^ 3 = 1000

This holds true of any of the subcomponents of a complex structure like the Eiffel Tower. So, it also holds true of the entire tower, which is just the sum of its subcomponents.

The important thing is that Hilmar specified that all dimensions are scaled exactly, and that materials are the same as the original. So, model mass = original mass * ((model height / original height) ^ 3)

In our example, original mass = 8000 tons (assume metric tons, 1 mt = 1000 kg), or
original mass = 8,000,000 kg

So model mass = 8,000,000 * ((0.3m / 300m) ^ 3) = 0.008kg = 8 grams

If materials weren't the same we could factor that in as well. Suppose we used balsa (specific gravity 0.2) instead of iron (specific gravity ~7.5). Then the model mass would be

8 * (0.2 / 7.5 ) = 0.21 grams.