![]() Submerging the tube means displacing a large volume of water and of course water is relatively dense. ![]() The air occupies a lot of space with very little density. To submerge an inner tube filled with air under water comes from the fact that For example, the tremendous force required More generally, this method of relating volumes and density relates to otherĮxperiences in students' lives. Not change but the graph would no longer be linear in part (c). The question could also be formulated in terms of the relative percentages of Relative percentages of silver and gold by volume in the crown. The problem asks students to find the amount of water displaced given the ![]() The teacher may wish to share the picture at the beginning of the solution with students to help them visualize Archimedes' idea. Work as there would be a third volume $V_3$ involved and a more complicatedĪlgebraic expression relating the composition of the crown to its density. Lead, a much cheaper but also very dense material, the argument would no longer That the crown is made of gold and silver alone. In practice, Archimedes' method requires knowing The problem combines the ideas of ratio and proportion within the context of density of matter. Shouting ''Eureka!!!'' (I have found it) reportedly occurred after he solved this problem. The famous story of Archimedes running through the streets of Syracuse (in Sicily during the third century bc)
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