The volume of the tank isn’t the issue. The tank itself is rigid and at way higher pressure than the surrounding water at depth, otherwise the air wouldn’t come out.
Instead the issue is that the air is trying to fill the diver’s lungs and the diver themselves are somewhat squishy. In order for them to be able to inhale against ambient water pressure the air supplied must be of a matching pressure, which means a higher relative surface volume in each breath at depth.
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