If you want exact air space, What I do is draw it up on autocad and let the computer figure what the area of the triangle is and then multiply that by the internal width and divide that by 1728. I just draw in what width of wood I'm using.
Math is okay for simple boxes like rectangles and even this box which is a rectangle and a triangle really. But the cad is unbeatable for the more complicated boxes.
I drew yours up real quick and here's what I got.
If you use all 3/4" material, the exact volume is .98365 cu.ft. Not including bracing or sub displacement.
If you use all 1/2" material, the volume is 1.1341 cu.ft. not including any bracing or sub displacement.
I can also do all 5/8" or combinations of 3/4" and 5/8", etc, etc.