An Olympic weightlifter asked me this question and it has been bugging me for a couple of days now.
Suppose "lower part" is defined as anything below and including the hip. This means that the majority of the mass and density is determined by the muscles and bones of the legs and hips.
I've been trying to solve this via the relationship between the mass, density and volume of an object, using Archimedes' principle, etc.
While this approach can find the density and volume of the whole body, it can only give us the volume of the lower part, with the lower body mass and density remaining unknown.
Approximating the lower body mass via the lower body volume and the total body density would not be appropriate, since there's bound to be major differences in density - the legs are mostly skeletal and muscle tissue, while the upper body hosts most of the major organs.
Is there another approach that may yield the correct answer? Maybe measuring the conductivity of only the lower body would give a better estimation of its density, but how do we measure that?
Note: I already asked if amputation is an option and the suggestion was not met with enthusiasm.