When we introduce a new concept in science the meaning should always come for first. Unfortunately when we started to talk about density many of you knew the term density and could correctly identify it as the ratio of mass and volume. While this is correct it does not further our understanding of density itself.
If you take several objects made from the same material and find their mass and volume respectively you will find that if you divide the mass by the volume the number that results from finding this ratio is the same for all objects regardless of their size. What is the meaning of this ratio? If you have a piece of aluminum with a volume of 3 cm3 and a mass of 24 g the ratio of mass and volume would be 8, for a 5 cm3 the mass would be 40g and the ratio again would be 3. Imagine now you had a piece of aluminum with a volume of 1 cm3, then its mass would be 8g. This should give us insight into the meaning of the ratio of mass and volume. If it is 8 for all aluminum blocks then it is not a coincidence that this is also the mass of 1 cm3. In fact this ratio can be interpreted as the mass of 1 cm3. Only after we find the meaning of this ratio should we give it a name, and this name is of course density. Now density has a meaning for us. The example above only works for solid pieces of aluminum, it would not work for Swiss cheese for instance. Why is that? Obviously, because of the holes. A block of Swiss cheese might contain several holes, which would affect the mass of the block. .
