# Density of Materials

Archimedes, The King of Syracuse and the Golden Crown…. Archimedes (287 – 212 BCE ) lived in Syracuse in Sicily, which in those days was a Greek Colony, with its own King. The King of Syracuse had ordered a new gold crown and had given his goldsmith the right amount of gold to make it. When the goldsmith brought the crown to the King it weighed the right amount, but some of his servants told the King that they had heard the goldsmith boasting that he had stolen some of the gold and replaced it with silver, so the crown was not pure gold but an alloy (mixture) of gold and silver.

The King sent for Archimedes and told him he was to find out whether this was true – but he must not damage the crown. Archimedes thought about the problem, which appeared quite impossible to solve, what would you do?

Density is simply a way of comparing how much mass you have for a fixed volume. We often use 1kg or 1g for this process. We also use cm3 or m3 for the volume.

Several useful equations for volume are…

The formula for density uses the greek symbol “rho” and we work out density = mass/volume

An example might be for Steel…. 8050 kg/m3 or 8.05 g/cm3