To kick things off, we can first calculate the weight of the materials used for the first floor of the building. We will then use this number and multiply it by the approximate number of floors for the empire state building. If you guessed the building had 100 floors, you wouldn't be far off as it has 102.
Let’s start with the first floor...
Total volume of the first floor
If the Empire State Building is square shaped, we need to guesstimate the height, length, and width of the first floor of the Empire State Building.
Generally, each office floor’s height is around 3.9 m. If you did not know that - its ok, you should be able to guess the height of an average human and double that. To estimate length of the Empire State Building, let’s assume that the building has 40k sq. ft of office space per floor.
Converting sq. ft to sq. meters, we get approximately 3.6k sq. meters of space per floor. Given its square shape, we get length and width of the building as 60 meters each.
We have the equation for the volume of the first floor of the Empire State, which is height*length*width.
Plugging in the above numbers, we get the volume of the first floor as 3.9*60*60 = 14,040 m^3.
Next, we assume that the Empire State Building's walls, pillars and the foundation is made of steel, cement and glass.
Assuming the volume consists of 10% of cement, 10% of steel and 5% of glass we get …
Weight of cement
Cement - If 10% of the total volume is cement than the volume of cement used is 10%*14,040 = 1,404 m^3
Now, if we don’t know the answer to how much 1m^3 of cement weights - that is something the interviewer should be able to help with and if you are close to the actual number i.e. 1 m^3 of cement weights 1.51 ton, he might even let it slide.
Ok so, the total steel cement to construct the first floor is 1,404*1.51= 2,120 ton
Weight of steel
Similarly, given that 10% of the volume of the building is steel we have...
1 m^3 of volume of steel weights 7,800 kg or 7.8 tonnes
So, the total steel used to construct the first floor is 1,404*7.8=10,951 tonnes
Weight of glass
...and finally, for glass we compute.
Converting to tones, 1 m^3=2.49 ton (for the glass),
So, the total weight of the glass used to construct the first floor is 702*2.49=1,748 ton
Total weight of the first floor
By adding weight of steel, cement and glass, we estimate the total weight of the first floor of the Empire State Building as ...
2,120 + 10,951 +1,748 =14,819 ton.
Total weight of the Empire State Building
Finally, we can estimate the weight of the Empire State Building by multiplying the first- floor weight by the number of floors i.e. 102.
Answer: The weight of the Empire State Building is ~1.5m ton.
*** this is the weight of an empty building and we can always add weight for things like tables, chairs and computers among others.
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