The sphere and cylinder
In the two books of the treatise On the Sphere and Cylinder, Archimedes performs a number of important demonstrations on the properties of these figures and the cone.
The model shows the ratio between the volumes of three solids - the sphere, the circumscribing cylinder and the cone with the same base and height as the cylinder. When the cylinder is completely full of sand, the device can be overturned to observe the sphere and cone fill up completely. As the volume of the cone is one third that of the cylinder, the volume of the sphere is clearly 2/3 that of the circumscribing cylinder and so twice the volume of the cone, as demonstrated by Archimedes.