Density questions 

The density questions below will help you understand deeply the meaning of density.

Bar of gold

Question #1: What will happen to the density of a bar of gold if it is cut in half? Will the density be half now? 

Answer: The density remains the same. The density will not be half of the original amount.

Let's do some math to make this clear.

Suppose the mass of the bar of gold is 50 grams and the volume is 2.5906 cm3

density =
mass / volume


density =
50 g / 2.5906 cm3
= 19.3 g/cm3

Bar of gold
After the gold bar is cut in half, the mass is 25 grams and the volume is 1.2953 cm3
density =
25 g / 1.2953 cm3
= 19.3 g/cm3

Question #2: Is a pure gold ring less dense than a heavy bar of gold? 

Answer: If you understood the answer for question #1, then the answer for question #2 should be straightforward.

The density of pure gold should not change unless it was mixed with another substance. Therefore, the gold ring and the heavy bar of gold have the same density. 

Question #3: Does 500 kg of diamond more dense than 1 kg of silver? 

Answer: Silver is always denser than diamond. Period.

Tricky density questions.

Question #4: The density of platinum is 21.4 g/cm3 and the density of steel is 7.8 g/cm3. Which one has more volume-1000 grams of platinum or 1000 grams of steel?
If    7 =
21 / 3
then,    3 =
21 / 7

Similarly,

If    density =
mass / volume
then,    volume =
mass / density


volume of 1000 grams of steel =
1000 g / 7.8 g/cm3
= 128.205 cm3


volume of 1000 grams of platinum =
1000 g / 21.4 g/cm3
= 46.72 cm3

As you can see, the denser material has less volume in this case.

In general, when two materials have the same mass, the denser material has less volume.

Question #5: The density of water is 1 g/cm3 and the density of ice is 0.92 g/cm3. Which one has more weight-3 liters of water or 3 liters of ice?  

This question is similar to question #4 with the exception that this time one of the materials is a liquid. Without doing any calculation, since the density of ice is less than the density of water and the volume is the same, we can conclude that 3 liters of ice have less weight than 3 liters of water. 

This will also explain why ice float on water!

I hope the density questions above really helped you understand density.

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