When Does Air Weigh More Than Iron?

it is a fact that the air in a cylinder around the Eiffel Tower, 

 weighs more than the tower itself! in our upcoming trip, one place we want to visit is the Eiffel Tower so we have been looking at it before our visit and found this fact, that’s right, if cylindrical tube were placed over the tower, the weight of the volume of air inside the tube would exceed that of the metal in the tower, from the article:

The density of wrought iron is approximately: 7.70 g/cm3

At a weight of 7,300 tonnes, this amount of iron has a volume of approximately: 948 m3

If melted down into a sphere of iron, this ball would have a radius of just 6.1 m

If flattened into a coin with a diameter that circumscribes the base of the tower, it will be just 4 cm thick!

...Using the dimensions of the foot of the tower, the diameter of the cylinder can be calculated...

Knowing the height of the tower, combined with the disc diameter we determined above allows us to calculate the volume of the cylinder. There is approximately 7.96 million m3 of air in this tube. [adjusting here for the varying density of air at different altitudes] ...we can take a simple average for the density of the air to give a value of 1.19 kg/m3.

Multiplying by the volume we get a value of approx 9,400 for the mass of the air. Even with our approximations, this is certainly greater than the quoted 7,300 tonnes for the mass of the iron.

It's true - the mass of the air in the cylinder surrounding the Eiffel Tower, is heavier than the tower itself! I still can not get my head around this one, but according to the mathematical calculations it is true.