Density

Density is a measure of the mass per unit volume of a substance.

To calculate the density of an object you need two values: the mass and the volume. (Note that the weight is not the mass; weight is a force measured in Newtons, whereas the mass is how much matter there is in something.)

You can us a formula triangle, like the one to the left, to help you remember, all you have to do is cover the letter of the value you are looking forward. For example, if I was looking to find density I would cover the d leaving me with m/v (or, in other words, mass divided by volume). Same with if I wanted to find mass; I would cover the m leaving the d and v visible, so density multiplied by volume equals the mass.

Example 1

I have a hexagonal prism. The area of the cross section of the prism is 15cm squared. The length is 8cm. The prism is made from wood with a density of 0.8g/cm cubed. Work out the mass of the prism.

With questions including shapes they usually provide a diagram, however if they do not it is handy to draw a quick sketch to give you an idea of what it looks like.

This is my sketch to help me understand my object. Also extract important information from the question, you can do this by underlining, highlighting or rewriting it.

density = 0.8 mass = ? volume = ?

area of cross section = 15cm2

length = 8cm

Step 1: Work out the volume of the prism.

The question is asking me to find out the mass of the prism, however to do that I need the values of the volume and the density, but I only have the value of density. So that tells me I need to find out the volume as well.

Volume of prism = area of the cross-section x length

Volume of prism = 15 x 8

Volume of prism = 120cm cubed

Step 2: Work out the mass.

Now that I've worked out the volume I can now calculate the mass.

Mass = Density x Volume

Mass = 0.8 x 120

Mass = 96g

Note: Density can have two units, either kg/m cubed or g/cm cubed. Make sure to check which units you are using and to convert them if needed. In the example above the density is said to have been 0.8 g/cm3 meaning that the mass is in grams.

Now you try...

QUESTION 1

The mass of 5m cubed of copper is 44800kg. Work out the density of copper.

QUESTION 2

A solid cylinder is made from wood. It has a radius of 4cm and a height of 10cm. The density of the wood is 0.6 grams per cm cubed. Work out the mass of the cylinder. Give your answer correct to 3 significant figures.

Answers

Question 1: 8960kg/m3 (Hint: The mass is given in kg and volume is given in m3 so the units of density will be kg/m cubed.)

Question 2: 302g (Hint: Firstly, you need to work out the cross sectional area using the formula for area of a circle (πr squared) and then multiply that by ten to get the volume. Then use M= D x V to get the mass.)