Prism and pyramid weighing

Pictures

The volume of the pyramid is one third of the volume of the prism with the equal base and height.

This relationship can be using seesaw scale and objects made of homogenous material.

The key principle of seesaw scale is intuitively obvious: to balance a heavy body one needs to put the light body farther from the fulcrum.

Quantitatively, this principle is expressed in the fact that in the equilibrium position the relationship between the masses (therefore, volumes, since the objects’ densities are the same) is equal to inverse relationship of the distances from the fulcrum to the bodies being weighed.

In the case given, the pyramid should be placed three times as far as the prism.

Note that this volume relationship is valid for pyramids and prisms of equal heights with arbitrary equal bases.