I was hoping to use Blender to calculate the mass of shapes with curved surfaces. To start I took a 1m cube and performed a boolean difference with a parabolic curve (x=0 to 1m)that was extended horizontally for 1m and removed the upper part of the cube.
The volume remaining is 1/3 m^3 (by basic integration of x^2 -> x^3/3). However, using the "calculate mass" option for rigid body under Physics properties, using lead as a material for the density. the mass of the cut object was 30.6% of the mass of a 1m cube also of lead - as opposed to the 33% I expected and hoped for.
I am trying to figure out where the error has occurred. The parabolic cut looks fine and so I think there must be an inaccuracy in the way Blender estimates the volume of shapes with curved surfaces.
Please could you tell me how Blender estimates the volume of an object when using the calculate mass menu item.
I have constructed scales in Blender using rigid body simulation and hoped to show Archimedes Method of Mechanical Leverage where integrated shaped (straight line slope to parabolic to cubic and so on - can be shown to balance). However, to do this convincingly, I need Blender to have more accurate mass estimation than I get here.