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

The increase in the Eiffel Tower's height with a 15°C rise in temperature can be calculated using the coefficient of linear expansion for steel, leading to a straightforward application of the formula ΔL = αL₀ΔT.

Step-by-step explanation:

The question you've asked about the Eiffel Tower is related to the concept of thermal expansion in physics. Specifically, you're interested in how much taller the Eiffel Tower becomes when it experiences a temperature increase of 15°C. Steel has a linear expansion coefficient, and when applied to the original height of the structure, this coefficient allows us to calculate the change in height due to thermal expansion.

To calculate how much taller the Eiffel Tower becomes, we use the formula for linear expansion: ΔL = αL₀ΔT, where ΔL is the change in length, α is the coefficient of linear expansion for steel (approximately 12 x 10⁻¶ /°C), L₀ is the original length (321 meters in this case), and ΔT is the change in temperature (15°C).

Answer 2

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* 324 m =7948168.803\ m^3`

Thus, the mass of the air in the cylinder,

`=1.225\ kg/m^3 * 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.