Answer:
By computing the crown's density.
Step-by-step 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:

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.