A subject high in my list of current interests is the measurement and the biological applications of the volumes of snail shells. Recent relevant posts are here and here.
The volume of a shell is a direct indicator of the amount of space the occupant snail requires. For that reason, I consider it a biologically significant property. However, shell volume is rarely used in research, probably because there is no easy way to measure it. One method that immediately comes to mind is to fill a shell with water and then to determine the volume of the water, preferably by weighing the shell before and after. However, this is easier said than done, because air tends to get trapped in the apexes of shells, which makes it very difficult to fill them completely with water. That's why empty snail shells float in water. Moreover, many field-collected shells have debris trapped in them, which also prevents them from getting filled completely. And because most adult shells are opaque, one can't see if a shell is clean or filled completely.
Here is a rare example of the use of shell volumes from the literature (Kemp and Bertnes, 1984).
This graph shows the relationship between shell volumes and shell lengths in 2 morphs of the intertidal snail Littorina littorea. The authors state that shell volumes were determined by "measuring the water holding volume" without additional details.
From general geometric considerations, volumes of snail shells (V) are expected to follow a power law in the form, V=cL3, where c is a constant and L is a linear shell dimension (for a relevant discussion see, Schmidt-Nielsen, 1984). If you take the logarithm of both sides of that equation, you'll get, logV=logc+3logL. In the graph above, the equation for line C was logV=-4.04+3.09logL. The equation for line E was similar.
Schmidt-Nielsen, K. 1984. Scaling: Why is animal size so important? Cambridge University Press.
Paul Kemp & Mark D. Bertnes. 1984. Snail shape and growth rates: Evidence for plastic shell allometry in Littorina littorea. Proc. Natl. Acad. Sci. USA. 81:811–813.