The goldsmith designed a beautiful crown of golden leaves for the king. The king was very impressed. He marveled at the crown, he weight to make sure all of the gold was used. The weight was the same as the punt that had been given to the goldsmith.
Later the king began to suspect that the goldsmith had mixed the gold with silver and and had not used all the gold that was given to him. He believed this to be true but had no way to prove it. King Heiro called upon his friend Archimedes to help him solve his problem. Archimedes knew the answer lied in the density of the metals. Since density is a physical property each had it's own specific density. Although a lump of gold and silver can be thesame size a lump of gold is twice as heavy as thesame size lump.of silver. Silver is lighter that gold.
He knew all these facts but he did not know how to find the density of the crown. While pondering on the matter, he decided to soak in the bathtub. He did his best thinking while soaking in the tub. He headed for the public bathto relax and think. While on the way he made a mental list of the facts. Mass can be determined easily simply place the crown on a scale. But it's volume, well that was a bit tougher. He arrived at the bath house just as a tub was filled to the brim. When he stepped into the tub some of the water spoiled out. The more he sank into the tub the more water spilled out. He realized that the amount that spilled ouist be exactly the same value as him.
All of the sudden Archimedes had a right idea. As of a light bulb flashed on on his mind. He had the solution to the King's problem. He was so excited and happy. In those days to disappoint a king could mean a loss of one's head. He began running through the streets without his clothes shouting, " Eureka, Eureka! " ( Eureka is the Greek word for " I Found it" )
Archimedes made two masses. The same mass as the crown, one in gold and one in silver. He then filled two containers to the brim with water. The amount of water that spilled out of each container was equal to the volume of each of the lumps. This is called the displacement method of calculating volume.
The amount of water displaced by the gold was less than that displaced by the silver. He filled one more vessel and stopped in the crown. Archimedes found that more water was lost with the crown than with pure gold. He calculated the crown was not made of pure gold. The goldsmith was punished for cheating the king.
Archimedes used the formula for density to solve the kings problem.
Density= Mass / Volume
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