The results of some back-of-the-envelope calculations:
- The air in the Empire State Building weighs about 4 million pounds.
- The energy consumption of the world’s population will be greater than the energy coming from the sun in less than 500 years. (Peak photons?)
What’s surprising about such estimates is how often they are very close to the reality. This is especially true in a multi-step approximation, where over- and underestimates at various steps tend to cancel each other out, usually resulting in something not too far off from the truth.
Both Microsoft and Google use questions like these as part of their job interview process. We did a bunch of them in my freshman physics class; I loved them.