Math CentralQuandaries & Queries


Question from Ed:

I am writing a science fiction novel that involves a spherical space station with a
radius of 800 meters. Inside, artificial gravity allows parallel floors set 4 meters
apart. If you count the floor that has a radius of 800 meters as Floor 0, then the
next floor up (Floor +1) would by 4 meters above the surface of Floor 0. There
would then be Floor -1 4 meters down from Floor 0. This would continue until
you reach the top or bottom floor, where there is at least 4 meters but less than
8 meters to the top or bottom of the sphere. Obviously the top and bottom
floors would have the (same) smallest area, while Floor 0 would have about 2
million square feet.

My problem is figuring out the total area of all of the floors, or for that
matter, any particular floors or the total number of floors (the total of all the
+ floors, the - floors (these numbers will be the same) plus Floor 0.

I tried using trigonometry couldn't derive the radius of any floor but Floor 0.
Unfortunately I never took calculus, so if it is required I am really SOL.

I would like the answers (total surface area of all floors and the number of
floors). However, I would like to find a way to figure out how big the area
of any specific floor is I also will need to make some floors not 4 meters
apart but another amount, to accommodate tall equipment such as the fusion
reactor. Thus if this reactor is the height of 14 meters, I'd have to know how
to say, for example, that specific floors don't exist; e.g., floors +6 has the
base of the reactor and floors +7, +8 and +9 are missing (and their area
would have to be deducted from the grand total of all floors.



Hi Ed,

In my diagram C is the centre of the sphere, B is the centre of some floor above C and A is a point on the circumference of this floor.

space station

CA is a radius of the sphere so its length is 800 metres, the length of BC is the distance between the floors and AB is a radius of the floor. Once you know the length of AB you can find the floor area.

ABC is a right triangle so Pythagoras theorem gives us

|AB|2 + |BC|2 = |CA|2.


|AB| = √(8002 - |BC|2) metres.

Good luck with the novel,

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