*Archimedes is said to have discovered the buoyancy rules, which are called Archimedes’ principle, when he was asked by the King of Syracuse in Sicily to determine whether a crown was pure gold, as the goldsmith said, or was an alloy. At that time no chemical means were known for settling the question without destroying the crown. Archimedes was struck with the idea of how to do so while taking a bath, and he jumped out of his tub and ran through the streets yelling “Eureka” (“I have found it”). The story goes that he was so excited that he did not bother to get dressed before doing this.

Suppose that in testing the crown Archimedes found that in air it had a weight of 5.0 N and a weight of 4.725 N in water. Assuming that the crown was made of gold or of silver or of an alloy of both, what percentage by volume was the gold? Assume that the density of gold-silver alloys is ρ_alloy = ρ_silver + (vol.% gold) · (ρ_gold − ρ_silver)/100. The densities of gold and silver are 19.3 and 10.5 g/cm³, respectively.