Going off of Jefferies' designs for the interior layout of the original Enterprise (limiting to areas that would allow someone to stand comfortably) we get approximately 613,500 square feet (more if we included the sub-deck area of the engineering deck in the secondary hull). Most of the decks of the primary and secondary hull are 10-12 feet heigh, the decks of the dorsal are about 8.5 feet heigh and the engineering deck is 20 feet heigh.
For comparison, my apartment is about 700 square feet, so the original Enterprise has about 876.5 times the footage of my apartment.
The original Enterprise is actually quite spacious. I've been using the
Booklet of General Plans for the
USS Saratoga, CV-60 for reference/comparison purposes and living conditions on the Enterprise are much nicer.
Living space would mean
after subtracting machinery spaces, turbolift shafts, fuel tanks, water tanks, engines, etc., yes?
We aren't given enough information to make those types of deductions, but this is how I approached this issue in my plans of the original Enterprise...
As far as living supplies and resources for the crew (food, water, clothing, misc. items), every crew member gets allocated about 1.5 times there body weight (mass) for these things. Because the Enterprise is a closed system the transporter would keep track of what you left with and what you came back with, so a significant difference would need an explanation if you didn't want it deducted from your allotment. So we're talking about approximately 1,617 cubic feet for raw materials for a crew of about 430. The people could comfortably live on much less (like 0.5 times there body weight), but this means that the Enterprise could support an additional 800 people in case of an emergency without over taxing the system.
Everything is recycled, elements that were part of your dinner one week might end up as someone's uniform the next and as part of someone else's specialty tricorder the week after that.
A lot of the space needed for fuel (mostly for the impulse engines) and other items take up the remaining volume of the ship outside of the minimum deck height areas. There are other areas (mostly in the secondary hull) for cargo/storage, and the bulk of the warp drive is in the nacelles themselves.
Fortunately the Enterprise is a wireless environment (for both data and energy transfers) which keeps the internal infrastructure pretty simple. It also means that most rooms are multipurpose by design. What was a briefing room can be converted into a lab/research center if needed, crew quarters can be converted to office space, etc. This type of versatility has been recently included in the design of the Ford class of aircraft carrier.
I try to avoid the specifics of how many things work to avoid
steampunking the Enterprise. Trying to overly equate the equipment of several hundred years from now with what we know today would be like attempting to equate our technology using what people knew of back in the 18th or 19th century. That is part of the reason I consider the TMP Enterprise to be a
steampunked version of the original Enterprise.