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Clarifications:

- We only need to find the weight of the empty building, capable of standing by itself, without any of its content that can be removed/replaced. So no windows, no furniture, no people, no electric wiring, no lights etc. If interviewer requests any of it to be included you can do an independent analysis for the same.

- Just the weight from the top floor to its bottom floor, so no weight of the foundation concrete base and parking space.

Assumptions:

- Most skyscrapers have a suspended weight somewhere in the top half to balance wind forces. This is considered and assumed to be around 700 tons. ( That's the weight of the famous suspended ball of Taipei 101 ).

- The needle at the top is around 300 tons

First Calculations:

Lets say the building has a 100 floors, a big hall/floor on the top, and the sky touching needle.

Focus on the floors for now. By looking at the building, floor changes width significantly around 5 times creating step like structures. Lets say it happens evenly along the height of the building. Each time a step happens, as we go down, increase the weight of the individual floor below by 40%. For every other floor, increase the weight of the individual floor below by 5%, because every floor below has to stand one more floor than the floor above, so more concrete and pillars.

Assuming the top floor weighs 100 tons, weight of 100 floors is

100*(1+ 5% + (5*5)% + ... + (30*5*5*...) + ...) ( I am skipping calculating this, you will need a calculator )

The hall at the top must be nearly 3-4 times the weight of the top normal floor. So 350 tons say.

The needle is probably around 300 tons. The suspended ball is 700 tons.

Second Calculations

The structure is a 400 m building of concrete with 30 m wide base. Assuming concrete density is 3 ton/cubic m and 80% of the 400m tall cuboid encompassing it is air(because of tapering nature towards the top to the needle and being empty inside), weight is

80%*400*30*30*3 tons

Sanity check:

Triangulate the weight with the 2 methods.

In the first method, except for the suspended ball, the needle and the top normal floor which are absolute estimate, all other estimates are relative and based on the weight of the normal floor. So you can adjust this number a little to make your answer a little more saner.