Gallons = cu ft * 7.48051948
spelled out that is the cubit feet you are testing times the 7.48 number (which is gallons per cubic foot)
As far as size try this http://www.aquaponic.com.au/backyard.htm there is spreadsheet there you can use to calculate the size of your system. If you dont have MS OFFICE get "open office" its an opensource app that will open the xls file.
Well that would depend on how deep your grow bed is.
In my estimation a 400 gallon grow bed is twice as big as a 200 gallon grow bed. I tend to use deep grow beds that are 100 gallons. (I use rubbermaid stock tanks as grow beds) I like to have twice as much grow bed volume as I have fish tank volume. The deep grow beds allow me lots of filtration though it does kinda reduce the number of bushy plants that one can fit in a grow bed.
I am hoping to have at least a 24 x 24 foot room devoted just to aquaponics. It will be a indoor atrium earth sheltered room with photo voltaic and solar hot water available to both heat the floor and provide hot water for heating fish tank when necessary
how many tilapia per person for what? To eat one every day? Every week? Every Month?
How many you should have in a 200 gallon tank also depends on how much filtration you have, how much in the way of backup you will have and how carefully it will be monitored. Very heavily stocked tanks can hit disaster mode very quickly. A few hours without pumping or aeration could kill all the fish quickly when heavily stocked.
In my experience, if you need to ask now many fish you can have in a fish tank, you are not prepared to handle the MAX. A more reasonable level is 1 fish per cubic foot of flood and drain media bed. Or about one fish per 7.5 gallons of gravel. That is figuring on fish that won't get over 1 lb. There needs to be enough fish tank to support those fish even when grow beds are flooded.
I actually stock 1 fish per 10 gallons of fish tank and 20 gallons of grow bed because I grow my fish big.