Archimedes’ principle describes a law of physics regarding how fluids interact with a solid body in their midst. It is, basically, the concept of buoyancy: A body immersed in liquid will be subject to upward forces equal to the fluid it displaces. This upward force is known as buoyancy, and it is what keeps ships, people and objects afloat.
In addition to being an early discovery in the study of physics, Archimedes’ principle also spawned a colorful story that is still told more than two millennia later. No contemporary accounts of Archimedes’ life survive, and this story may well have been created by fanciful historians of the Roman era. Galileo, writing in 1586, proposed that Archimedes could well have achieved the same result with a slightly more scientific method.
Archimedes lived in Syracuse, a Greek colony in Italy, in the third century B.C. He was one of the greatest scientists of ancient times, working in both theoretical and applied sciences. He invented devices for science and war and discovered the basic principles of mathematical calculus. While his inventions were better known than his theories during his lifetime, the reverse is true in modern times. The discovery of Archimedes’ principle is one of the bestknown stories about this great thinker.
According to a legend recounted by the Roman historian Vitruvius, the king of Syracuse challenged Archimedes to discover whether a crown was truly composed of solid gold, or if other metals had been added, as he suspected. Archimedes spent some time considering the problem, because he could not melt down or otherwise damage the crown to analyze its composition. The solution came to him in a flash as he was settling into a full bath and realized the water displaced from the tub was equal to the mass of his body. In a moment of inspiration, it is said, he knew he could solve the problem by immersing the crown. If it displaced less water than an equivalent quantity of gold, it contained other metals.
Archimedes is said to have been so elated by this discovery that he left his house, racing naked through the streets of Syracuse shouting, “Eureka!” This Greek word means “I have found it,” and is still used in modern times to denote a moment of enlightenment or discovery. The popular legend of Archimedes’ principle illustrates, and may have helped to establish, the common perception of the absentminded scientist who values knowledge and theory over social niceties such as clothing.
anon249806 Post 4 
The principle is based on density: weight per unit volume. Consider an object that sinks in pure water. What you know about it is that its density is greater than the density of water. Can you measure or estimate its actual density? (No, unless you want to get into sinking velocity.) Now consider an object that floats. Yes, you know its density is less than that of water, but what is the density? If the object is a perfect cube and you can measure the depth of submergence and the side length, that ratio is equal to the object's density divided by the water's density, hence you can calculate the object's true density. In Archimedes' crown displacement, he may have chosen to use a dense saline solution rather than pure water, so that the crown just barely floated and he could calculate the crown's metal composite density. 
anon200435 Post 3 
please post some buoyancy problems with their solutions.

bear78 Post 2 
@alisha I believe you can figure out both weight and density with Archimedes principle. Think of it this way when you put an object in water, it is going to bounce up depending on the weight. The force of that bounce is the weight of the object. The density of the object can be figured out by looking at whether that object sinks, floats or stays in between. Let's say you put something very heavy, it will sink to the bottom which means that the density of that object is more than the density of the water. If you put a piece of foam, it's going to float on the water, so that foam has very little density, less than the density of the water. If an object does neither, it probably has the same density as the water. Does that help? 
discographer Post 1 
This seems like a very straightforward principle but what I don't quite get is whether Archimedes' principle measures density or weight? I think it would be relatively easy to figure out weight for an object that sinks, but what about objects that float? How can I figure that out using Archimedes' principle? 