There is a story that Archimedes, the Greek mathematician, was asked to find out if the new golden crown of the king was made of pure gold, while keeping the crown intact. Sitting in a public bath and thinking about it, Archimedes noticed the displacement of the water caused by sinking his body lower into the water. He suddenly realized that he had found the solution: if the crown was made of pure gold, it should displace the same volume of water as a bar of pure gold with an equal weight. Excited, he jumped out of the bath and ran home shouting "Eureka!" ("I've found it!"), forgetting that he was still naked...

We do not know if the story is true. However, we do know that Archimedes discovered the first law of hydrostatics: when a body is immersed in a fluid, it experiences an upward buoyant force, which is equal to the weight of the fluid displaced by the immersed part of the body.

Can you solve the following questions and have your "Eureka!" moments, using this famous law?

In an aquarium filled with water, a block of ice floats. We mark the current water level.

The question: When the ice has molten completely, will the water level be higher, lower, or still the same?

The answer: Click here!

Another question: In an aquarium filled with water, a block of ice block floats, with a bar of gold frozen in it. We mark the current water level. When the ice has molten completely and the bar of gold has sunk to the bottom of the aquarium, will the water level be higher, lower, or still the same?

A hint : Click here!

Another answer: Click here!

Yet another question: In an aquarium filled with water, a block of wood floats. On top of the block of wood, a brick has been glued. We mark the current water level. If the block of wood is turned around (so that the brick hangs under it), will the water level rise, fall, or stay the same?

Yet another answer: Click here!

The fourth question: We have a pair of scales, with a block of lead on the left scale, and a block of wood on the right scale. Both blocks have the same weight, so the scales are in balance. We take the scales with the blocks and immerse them in an aquarium filled with water. Will the scales stay in balance, will they turn left, or will they turn right?

The fourth answer: Click here!

The fifth question: In an aquarium filled with water, a block of wood floats. On top of the block of wood, there lies a bar of gold. We mark the current water level. If the bar of gold falls into the water and sinks to the bottom of the aquarium, will the water level rise, fall, or stay the same?

The fifth answer: Click here!

The sixth question: In an aquarium filled with water, a sponge floats. While the sponge slowly absorbs water (but stays floating), will the water level rise, fall, or stay the same?

The sixth answer: Click here!