Question

The eiffel tower has a mass of 7.3 million kilograms and a height of 324 meters. its base is square with a side length of 125 meters. the steel used to make the tower occupies a volume of 930 cubic meters. air has a density of 1.225 kg per cubic meter. suppose the tower was contained in a cylinder. find the mass of the air in the cylinder. is this more or less than the mass of the tower?

Answer 1

Since the tower base is square with a side length of  125 m,

Therefore,

$(125\ m)^2+ (125\ m)^2=31250 m^2$

Square root of 31250 = 176.776953 (Diameter) , so this is the diameter of the cylinder to enclose it, and radius, r = 88.38834765 m and height, h = 324 m.

The volume of cylinder,

$=\pi r^2h=3.14(88.38834765 m)^2\times 324 m =7948168.803\ m^3$

Thus, the mass of the air in the cylinder,

$=1.225\ kg/m^3 \times 7948168.803\ m^3=9736506.78\ kg$

Hence, the mass of the air in the cylinder is this more  than the mass of the tower.