[Doxin]

You'd only need as much air volume as you have volume of things heavier than water. A boat sinks because air is displaced by water, increasing the density of the boat. If you make sure the displaceable air runs out before the density of the boat is higher than water it'll never sink.

In practice this is something that's actually done quite a bit. Fill a lot of air spaces in a boat with foam and you get to the point where if your boat fills with water you can simply pull the plug in de bottom of the boat and it will un-sink itself most of the way. You see this for example on small sailboats, the only caveat being you can't be on the boat as it's un-sinking since you'd weigh it down.

That said, seems to me that foam is a lot cheaper and easier than micro-engineering every surface on the boat.