>>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.
>
>Thanks.
The answer is found in Calculus. The shape of an object of an arbitrary shape can be obtained through integration. The basic idea is to (mathematically) slice the object into thin slices, calculate the surface area of each piece and multiply it by its thickness, and add everything up. (The area of a thin slice, of an arbitrary form, is also calculated through integration - cut it into thin strips, and use the formula of the rectangle for each strip.)
For many shapes that can be defined through equations, a mathematically exact solution can be found, by analyzing what happens when the pieces get thinner and thinner, "approaching zero". In other cases, numerical integration is used, i.e., actual strips are calculated, making them thin enough to get the desired accuracy.
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