As I understand it, there are two different general models for specifying the size of tanks.
The european or metric approach specifies the actual internal volume of the tank, e.g., 12 liters. If you took the valve off, filled it with water, and poured that into a measuring container, that's what you'd measure.
The US or imperial approach specifies the amount of 1 atm air that will be contained in the bottle at the working pressure. You can tell with common sense that an al80 doesn't have an internal volume of 80 cubic feet, so that 80 means something else. What it means, using the nominal numbers we generally use, is that if an al80 is filled to its working pressure of 3000 psi, it will contain the same gas that will occupy 80 cubic feet at 1 atmosphere (about 14.7 psi).
So you need two numbers, the tank cubic feet rating and the working pressure at which that cubic foot rating is made.
Your examples are about right, although if you search around you'll find some tables with more precise values, for example, a standard al80 actually holds something like 77.5 cubic feet of 1-atm gas at 3000 psi.
OK, look here for example:
Scuba Cylinder Specification Chart from Huron Scuba, Ann Arbor Michigan
