The density questions below will help you understand deeply the meaning of density.
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
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.
As you can see, the denser material has less volume in this case.
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.