Answer
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Work Step by Step
Archimedes' principle states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. In simpler terms, it means that any object submerged in a fluid will experience an upward force that is equal to the weight of the fluid it displaces.
Archimedes would have required to estimate the crown's density to determine whether it was made of pure gold or a gold-silver alloy. He might achieve this by calculating the weight and volume of the crown. He was unable to harm the crown, nevertheless, in the process.
Archimedes understood that he could determine the volume of the crown without harming it by applying the buoyancy principle. He measured the volume of water after adding it to a container to a specified level. He next dipped the crown in water and measured the additional amount of water that was displaced. The crown volume would be different between the two volumes.
Next, Archimedes weighed the crown and calculated its density by dividing its weight by its volume. He then compared the density to that of pure gold to determine whether the crown was made of pure gold or a gold-silver alloy.
Legend has it that as Archimedes performed this experiment, he realized that he had found a way to measure the volume of irregularly shaped objects, not just those with regular shapes. He is said to have been so excited that he ran through the streets shouting "Eureka!" (meaning "I have found it!").
