I overheard one pupil tell another yesterday morning that:
“The air in a cylinder that contained the Eiffel Tower
would weigh more than the Eiffel Tower itself.”
It sounded feasible, but I wanted to check the maths.
The metal structure of the Eiffel Tower has a mass of 7300 tons, or 7.3 million kilograms. The design of the tower is very space-efficient: if you melted down the pure iron* that it is made of, it would occupy a volume of only 930m3, equivalent to a sphere with a radius of just six metres.
The Eiffel Tower is 324 m tall and sits on a square base with sides of 125 m. It would therefore fit inside a cylinder with a radius of 88 metres, giving the cylinder a volume of just under eight million cubic metres. This much air would have a mass of 10 million kilograms.
So yes, that pupil was telling the truth. The air contained in a cylinder that could hold the Eiffel Tower would be 2.7 million kilograms heavier than the Eiffel Tower itself.
I am particularly fond of the Eiffel Tower as it lists, around its base, the names of seventy-two important French scientists, mathematicians and engineers, including Ampère, Arago, Becquerel, Daguerre, de Coulomb, Foucault, Fourier, Fresnel, Gay-Lussac, Lagrange, Laplace and Poisson.
* More accurately, the tower is made from puddled iron, a type of wrought iron that has a density of 7850 kg/m3.