CHAPTER 3
3.5 Density and flotation
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1. Eureka! Archimedes and the fake gold crown
Read the following text and answer the questions.
Archimedes was a famous philosopher who lived in Syracuse (Sicily) about 2300 years ago. King
Hieron II ruled Syracuse. Archimedes was employed by the king to find a way to determine
whether his gold crown was made of pure gold or whether it was a gold alloy. Archimedes had to
find a way of solving the problem without damaging the crown. The solution to his problem came
whilst he was lowering himself into his bathtub that was filled to the brim with water. He observed
that the water overflowed as his body became submerged and he thought that this principle could
be used to solve the problem. He obtained a piece of pure gold of the same mass as the crown and
then placed it in a vessel filled with water. He collected the water that overflowed and measured its
volume. He repeated the experiment with the crown and found that the volume of water that
overflowed was not the same. He also used a simple set of scales to weigh the lump of pure gold
and the crown when they were both submerged in water. He found that the pure gold was heavier
when submerged than the crown. He concluded that the crown was made of gold alloyed with
cheaper metals such as silver.
(a) Calculate the volume of a 1000 g lump of pure gold given that its density is 19.3 g/cm3.
m 1000

 51.8 cm3
D 19.3
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V
(b) Calculate the volume of a 1000 g lump of pure silver given its density is 10.5 g/cm3.
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(c) Use your results in questions (a) and (b) to explain the results of Archimedes’ water overflow
experiments.
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(d) Archimedes proposed that the greater the volume of water that a body can displace, the lighter
it will weigh in water. Explain the results of Archimedes’ experiments on weighing the piece
of gold and the crown while submerged.
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2. Flotation
Steel has a greater density than water, while ice is less dense than water. Explain why a ship and an
iceberg both float in water.
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Core Science Stage 4 Student Worksheets