1. The Tale of this brilliant man and how he discovered the Archimedes Principle

2. Greek City of Syracuse This ancient city had been at war. Hiero was elected commander. In 265 Bc, Hiero led the Syracusans to victory against their enemies. The people of Syracuse chose Hiero to be their king.

3. Praise to the Gods Hiero was grateful to the gods for his success and good fortune. He decided to place a golden crown in the temple in honor of the gods.

4. Making of the Crown Hiero weighed out a precise amount of gold and recorded the weight.* He appointed a goldsmith to make the crown. It was to be fashioned into a wreath worthy of the Gods.

5. The Crown is Delivered On the appointed day, the goldsmith delivered the crown! It was an exquisitely-wrought crown shaped like a laurel wreath. It had the exact weight as the original gold nugget the king had given him. The king paid the goldsmith handsomely.

6. Preparation for the Ceremony Hiero was busy with his preparations for the wreath ceremony. A few days before the ceremony, he heard rumors that the goldsmith had cheated him by replacing some of the gold with an equal weight of silver.

7. Seeker of Truth Hiero was furious to learn that he may have been tricked! But, he was a fair-minded man. He wished to determine the truth before he punished the goldsmith.

8. Punishment? If the goldsmith had cheated him and mixed silver with the gold, then he would have to be punished. A crown that was not pure gold could not be offered to the gods.

9. An Offering to the Gods If the goldsmith had been honest, then the crown remained what it had intended to be, a sacred offering. If this was so, it should be placed in the temple as planned. Hiero needed to find out the truth quickly.

10. Archimedes Hiero believed there was only one man in Syracuse capable of solving his problem. His cousin, Archimedes, was a young man of 22. Archimedes was renowned for his work in mathematics, mechanics and physics.

11. Eureka Pondering how to solve the kings problem, Archimedes went to the public bath. As he began to lower himself into the water, the water began to spill out over the sides. He realized he had found a solution to Hieros problem He was so excited he jumped out of the tub and shouted, Eureka which in Greek means, I have found it!

12. Solution Archimedes knew it could be solved using density. A piece of gold weighing a certain amount would be smaller than a piece of silver weighing the same.

13. Density If the goldsmith had stolen some of the gold the king had given him, then the total volume of the gold + silver crown would be greater than the volume of the original amount of gold. The volume could be found by how much water it displaced.

14. Bucket approach Archimedes filled a bucket of water and filled it to the brim. He then measured how much water spilled out when he added a lump of gold the same weight as the one he had given the goldsmith.

15. You are Archimedes Now is your chance to play the part of Archimedes. Gold has a density of 19 grams per cubic centimeter. Use the displacement method to figure out the density of the new crown.

16. Alas! Now that you have calculated the density of the crown, you know whether or not Hiero was cheated. Tell whether or not the king was cheated by the goldsmith. Give quantitative observations for your reasoning.