Pi/6 is used under the assumption that a testicle resembles a
prolate spheroid.
The volume of a spheroid is given by: 4/3 pi a b c where a, b, and c are radii corresponding to lenght, height, and width. While measuring, we obtain diameters that have to be divided by 2 to be converted to radii that can be plugged into the equation.
Therefore, using diameters, the equation becomes pi/6 l h w or 0.52 l h w.
However, testes are rarely perfect spheroids. Depending on the shape of a given testicle the correct value of the constant will vary: elongated testes that tend to taper at the ends would better resemble a spheroid and would be best represented by a low constant around 0.52. More boxy/rectangular testes would be best characterized by a higher constant.
All the studies I have read state that 0.71 as the constant on average gives more accurate results than 0.52 when a comparison is made at autopsy (volume by water displacement).