In a rigid airship, the lifting gas is usually contained in smaller balloon-like cells inside the frame, which do not fill anywhere near all the available space

In a rigid airship, the lifting gas is usually contained in smaller balloon-like cells inside the frame, which do not fill anywhere near all the available space. Your estimate is probably considerably over, though your concern is still reasonable. (EDIT: they're not called ballonets; ballonets are used to maintain pressure in a non-rigid airship.)