I'm sure the half angle would be useful, if not indispensable, in determining the missing volume. I the angle is not constant, then it becomes an interesting question of which angle and how much and when which angle applies. Then there is the tricky questions of what constitutes the effective volume, which will depends on reed displacement which varies with reed strength and embouchure. Then there are the reed mechanics, which tend to lower pitch, and ambient temperature and gas composition, all three of which affect pitch independent of mpc volume, and the last two of which are often present as a gradient within the air column. The point being that if you try to quantify things, there is a lot to consider in trying to come up with operative numbers that will predict empirical results. But you will certainly learn something, at worst that your work is inadequate to come up with good results.