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Reasonably housing a billion students

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In my world (set in the near future - no magical tech), every child after reaching the age of 1, is sent to study for 15 years in a centralised location shared by the entire world. With some playing around with numbers and assuming controlling governments having control of population, I've calculated that it'll work out to be around a billion people.

The centralised location is very spartan, and aside from having a bed, a desk and chest, everything else is shared (so public bathrooms, communal eating areas etc). There'll be the bare minimum required to sustain lives (so exercise areas etc...), as well as lecture rooms and the like.

Resources and other needed requirements aren't produced on-site - rather they're shipped there, so no need to take that into consideration. Academic and non-academic staff (no idea how to estimate this) would also need to be housed.

So the question is, how much area am I going to need to house these billion students + supplementary staff?

I've tried to produce estimates based on prison densities, but these apparently vary widely, and I've gotten values from 70M km^2 (around the size of Lithuania) to 262M km^2 (around the size of the UK). Can anyone help put me on the right direction?

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This post was sourced from https://worldbuilding.stackexchange.com/q/40235. It is licensed under CC BY-SA 3.0.

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