P3 C) Density – Part 1
Density is the degree of compactness of a substance. Density is a measure of mass per volume and the usual units are g/cm3 or kg/m3. Density is calculated by dividing mass by volume. The formula triangle for density is shown below:
Let’s now have a look at some density calculations.
A 2.8 m3 block has a density of 3,250 kg/m3. What is the mass of the block? Give your answer in kilograms.
The question is asking us to work out the mass of the block. We find the calculation that we need to undertake to find the mass by covering up mass (m) in the density formula triangle. When we cover up mass, we see that we find the mass by multiplying the density by the volume.
We are given the density in kg/m3 and the volume in m3. Both of these units are consistent, which means that we can sub the values from the question into the formula; we sub the density in as 3,250 kg/m3 and the volume in as 2.8 m3.
A block of aluminium has a mass of 756 g and a volume of 280 cm3. Work out the density of aluminium giving your answer is g/cm3.
We can work out density by dividing the mass by the volume.
We are asked to work out the density in g/cm3. In order to obtain this unit for density, we need to have the mass in grams and the volume in cm3. We are told that the mass of the aluminium block is 756 g and the volume is 280 cm3. These values are in the correct units, so we can just sub them straight into the calculation.
This tells us that the density of aluminium is 2.7 g/cm3.
Sometimes you may need to work out the volume of a block (or other shape) before being able to work out its density. This will be the case for the next example.
An iron cube has lengths of 3 cm. The mass of the iron cube is 212.22 g. Calculate the density of iron. Give your answer in g/cm3.
The question is asking us to work out density, which we do by dividing the mass by the volume.
We have been given the mass of the cube in the question; the mass is 212.22 g. We are not given the volume, but we do know that each side of the cube is 3 cm. To find the volume of the cube, we either cube one of the sides or we multiply the length by the width by the height.
We now have the volume of the cube, which means that we can work out the density by dividing the mass (212.22 g) by the volume (27 cm3).
The density of iron is 7.86 g/cm3