For the past several weeks I have been trying to develop a method to measure the volumes of snail shells. The method I am working on involves the immersion of an object with an unknown volume in water and several sets of weight measurements. The method is not yet applicable to snail shells, because I can't quite figure out how to seal their apertures in a practical and reversible way so that water won't leak inside. Nevertheless, I have carried out a test using 6 small balls, including 3 balls from old computer mice, 1 metal ball bearing and a glass marble.
After I measured the volumes and the diameters of the balls, it dawned on me that I could use the data to calculate a value for pi. Here is the plot of measured volumes against measured radii.
This plot is, of course, based on the equation for the volume of a sphere: V=(π4/3)r3. Therefore, pi can be calculated from the slope. The value I got was 3.16, which is 0.6% higher than the true value of 3.14.
There are several sources of error that could have resulted in my erroneous result. For example, if the calipers I used to measure the diameters were off by even 0.1 mm, that could have created an error of about 0.4%. Also, the balls I used are probably not perfect spheres. Another likely source of error is the value I used for the density of water, which depends on the temperature and the purity of the water used.
If and when I figure out how to apply this method to snail shells, these errors will not be important as long as they are equally applicable to every specimen; I am mainly interested in the relative volumes of a sample of shells rather than the absolute values of their volumes.
Tests are continuing.