[(E)]

Assumptions
Artificial gravity
Ultratech hydroponics/psuedo native environment.

Running two outer spin gravity floors at about 10 meters in height and 160 floors of similar height oriented with up and down towards the ends of the cylinders. We end up with a population of something like 55000 per cylinder or an area of 5.8 square miles of floor space per cylinder. For arguments sake let's say cryo sleep etc enhances the first generation's growth rate to 1000% which counters out a 90% reduction due to loss of life as a result of the Ark's destruction as well as unoccupied space. That gives us about one million cylinders required. Arranged as a series of rings with 3141 in each ring it is about 320 miles long and 500 miles across with a lot of empty space in the middle.

If people agree with these numbers I'll edit the older posts to match.