Question

According to legend, archimedes, who was a famous greek mathematician, was given a crown, which was supposed to be made of pure gold but contained some silver alloy, by king hiero ii of sicily. he was asked by the king to prove or disprove his suspicion. (the crown indeed did contain silver). if you were archimedes, how would have determined experimentally whether or not the crown was pure gold?

Answer 1

Answer:

By computing the crown's density.

Explanation:

Hello,

In this case, considering Archimedes principle, it would be convenient to take the crown and place it into water by using a volumetric cylinder in order to measure out the displaced volume which matches with the volume of the crown. Then, by using a balance, its weight will be measured.

Now, according to the fomula:

$\rho =\frac{m}{V}$

The density of the crown will be computed. Afterwards, the computed density will be compared with the theoretical density of gold in order to determine whether the crown is pure gold or not.

Best regards.

Answer 2

Determining the volume of water displaced by the crown and using the gold density to determine the mass of the crown equals the mass got from weighing the crown on a weighing machine. if the mass matches the mass got from the weighing machine then the crown is made of pure gold if otherwise, the gold is not pure.