Eureka! Eureka!

Suppose that the crown should have been made out of 1kg of gold. What would have happened if the goldsmith had substituted half of the gold with silver?

If we compare the volume of 1kg of gold with the volume of 1kg silver we will find out that the volume of silver is approximately the double volume of gold (see picture above).

If the goldsmith had stolen half of the gold, he would have had to mix 0,5 kg of gold with 0,5 kg of silver (see picture above) so that the crown still weighs 1 kg and nobody would wonder about it (see picture below).

If we compare the volume of 1 kg of gold and the volume of the 1 kg mixture of gold and silver we will find out that the mixture has an higher volume than the pure gold (see picture below).

What did Archimedes has to do to test if the crown was made out of pure gold, without damaging it?

• a) He put the crown on scales to measure its weight.
• b) He submerged the crown into water to measure its volume.