How accurate do you want the answer? This is the 'easy/accurate-ish' way of calculating it (assuming air behaves as an ideal gas, which it technically doesn't). The 'complicated/more accurate' way is too much for me to remember...
Weigh the tank empty (or close to, as in after a dive).
Weigh the tank full (or at least have some pressure in it).
The difference is the mass of the air. You know (or can measure) the change in pressure and the change in mass of the air inside and can thus calculate the volume.
Example (Metric, sorry to those in the imperial world - I don't know the ideal gas equation in imperial. Can always convery pounds to kg, psi to bar then convert litres to whatever you like at the end).
Mass (Fulll): 18 Kg
Mass (Empty): 16 Kg
Change in Mass: 2 Kg
Pressure (Full): 200 bar
Pressure (Empty): 50 bar
Change in Pressure: 150 bar
Now using the magic formula P*V = m*R*T, where:
P = Change in Pressure (MPa)
V = Volume (Litres)
m = Change in Mass (Kg)
R = Ideal gas constant (0.287 kJ/Kg-K for air)
T = Temperature (Kelvin) (Room temp ~ 293 K)
So, rearranging to make V the subject.
V = (m*R*T)/P
V = (2 * 0.287 * 293)/15
V = 11.2 Litres
Now, you want your answer in cubic feet?
Well then;
Gas Volume = Tank Volume * Pressure
So we have 11.2 * 206 = 2307.2 litres
1 litre = 0.035315 cubic feet,
so we have 2307.2 * 0.035315 = 81.1 cubic feet
