Archimedes supposedly determined a gold crown was actually silver/gold? How did he know?

Question

Archimedes supposedly used the water-displacement method to establish the volume displaced by the crown, but wouldn't the volume be the same for either a silver/gold crown and a solid gold crown? How could he distinguish the two?

Answer 1

Because of the weight of gold itself, were you to have a large tub of water that had an overflow spout, under which spout there was a container to catch all the water that overflowed, you could fill the tub to the top with water, then having a dish within the tub that was floating free, by placing a gold crown in the floating dish there would overflow out of the tub of water an amount of water equal in weight to that of the crown. By weighing the water that came out of the tub, a person would know how much gold a crown was formed of.

The story says that the maker of the crown used a particular amount of gold. Were he to have used silver as a mixture it would have showed up as there being less water coming from the overflow.

The story is but an illustration of how Archimedes solved this particular problem.

Answer 2

If both crowns had the same weight, they would occupy different volumes (and displace different amounts of water) because pure gold and gold/silver have different densities.

Since density is mass divided by volume. If the mass is constatnt and we know that the densities must be different then the volumes must also be different.

Answer 3

archemedies calculated the volume that each (silver/gold crown& solid gold crown) displaced dividing its mass by this volume he found the difference in their dencities.the percent of silver in gold crown could then be easily found (dpure-dimpure)/dpure

Answer 4

I do no tunderstand it either. It makes no difference what mass the object has, it can still displace numerous verieties of volume.
Example, two identicle anchors. both are sunk, and displave water, but one has empty milk juggs (air tight sealed) attatched. they would both sink and have similar masses, but far different water displacements...