I'm afraid that I am too stupid to provide you with a mathematical explanation. However, I think you will agree that 10 kg of maize kernels has considerable less bulk than the same 10 kg milled into maize meal. Simply due to the additional air pockets. Conversely, the mass of 10 mL of sand is appreciably more than 10 mL of clay soil. Hence the use of sample density to estimate clay percentage.