This video will explore this fabled Archimedes’ concept using experiments and math. We will begin with a brief introduction to the problem that Archimedes faced – that is, determining the density of an irregularly shaped object. Why does density change with different materials? We will explain what the basis for density is and show examples of different objects with the same volume, but with very different masses. During this demonstration, we will show on the blackboard the relationship between mass and volume to density.

But how do we measure the volume of an irregularly shaped object? We will then describe how Archimedes solved the problem and prove this fact with a set of experiments. We will have an object of some material, such as clay, which will be in an unfamiliar shape. By taking a beaker filled with water, we will submerge the clay object and record the volume change. Then by taking its mass, its density can be determined. In order to verify the density measurement, the object will be reshaped in front of the camera into a cube and the density will be measured by taking its dimensions (and mass will have remained the same). Then, as a final verification, we will submerge the cube in the beaker and verify that the water level change is identical as before and ‘Eureka!’ we can determine density of irregularly shaped objects just like Archimedes.