# Understand Density

In this worksheet, students will learn how to measure density and use the density equation. Key stage:  KS 4

Difficulty level:   ### QUESTION 1 of 10

In this activity, we will be defining density and explaining how to measure it. Density is a measurement of the mass of each particle within a certain space.  If you have a lot of heavy particles in a space of 1 cm3  then you will have a high density, but if you have only a few light particles in 1 cm3 then you will have a low density.

The easiest way of picturing this is by looking at the models for solid, liquid and gas particles.

In a solid, the particles are close together in a regular lattice. They are vibrating all over the place but they tend to stay in their one specific spot. This makes solids denser because there are a lot of particles in a small area. What do you think about liquids and gases then?

In liquids, the particles are all touching still but they are free to flow over each other. This can lead to small gaps forming in their shapes and that means that you can’t fit as many particles into the same space. This means that the density is slightly less than that of a solid.

In a gas, the particles are free to go wherever they want - they tend to move quickly and have large gaps between them. This means that they have a low density because the particles are far apart.

So that's density – but how can we measure it?   Fortunately, there is a very important equation to help us out here:

density = mass ÷ volume

ρ = m ÷ V

That funny sign (ρ) is the Greek letter rho which, in this case, means density. Density is measured in kg/m3  (kilograms per metre cubed), mass is measured in kg (kilograms) and volume is measured in m3 (metres cubed).

Let's have a look at how we can use this equation to find the density of an object. By looking at the equation, we know that in order to work this out, we have to know its mass and volume.

Working out the mass is simple - you just need to put the object on a top pan balance and read off the measurement that it gives you (making sure that you zero the balance to start off with). Let's say that the object weighs 0.5 kg.

The volume isn’t all that difficult either -  all you need to do is measure the length, width, and depth of the object. You then multiply these numbers together and you get your volume. Let's say your object measures 0.25 m x 0.25 m x 0.3 m =   0.018 m3

So, put this into the equation:

ρ = m ÷ V

density = 0.5 ÷  0.018

density = 27.77 kg/m3

DON’T FORGET the units! Always put them in unless the question tells you otherwise!

And that’s it! Now you are a master of density! Let’s put your newfound knowledge to the test!

Select the correct definition for density from the list given below.

The number of particles in a given space

The mass of all of the particles in an object

The amount of space an object takes up

The amount of mass per unit area

Which of these states of matter has the highest density?

Solid

Liquid

Gas

Match the symbols to the units for the density equation.

## Column B

Density (ρ)
Kilograms (kg)
Volume (V)
Metres cubed (m3)
Mass (m)
Kilograms per metre cubed (kg/m3)

An object has a mass of 0.1 kg and a volume of 0.4 m3.

Calculate the density of the object.

## Column B

Density (ρ)
Kilograms (kg)
Volume (V)
Metres cubed (m3)
Mass (m)
Kilograms per metre cubed (kg/m3)

An object has an original density of 1 kg/m3 and is then heated. Its new volume after heating is 0.8 m3.

Calculate the change in density of the object.

Object mass = 2 kg.

## Column B

Density (ρ)
Kilograms (kg)
Volume (V)
Metres cubed (m3)
Mass (m)
Kilograms per metre cubed (kg/m3)

What happens to the density of an object when you cool it?

It increases

It decreases

Nothing

An object is heated.

Describe  and explain what happens to its density by talking about the particles.



Describe how to calculate the volume of a cube.



Calculate the density of this cube.

Its mass is 0.1 kg. Put these objects into order with the most dense at the bottom and the least dense at the top.

## Column B

Least dense
Oxygen
In the middle
Ethanol (alcohol)
Most dense
Aluminium
• Question 1

Select the correct definition for density from the list given below.

The amount of mass per unit area
EDDIE SAYS
This is one of those definitions that you need to remember - you'll find there are a lot of these in science. They are important because, when we say things in science, we need to be very specific about what we mean. So, if a question asks you about density, then you must be able to give the definition.
• Question 2

Which of these states of matter has the highest density?

Solid
EDDIE SAYS
The particles in a solid are tightly packed together in a regular lattice. This means that there are a lot of them in a small space. When something is dense, there are a lot of particles in a small space - so this definitely applies to solids. Their regular shape means that they literally cannot fit any more particles in!
• Question 3

Match the symbols to the units for the density equation.

## Column B

Density (ρ)
Kilograms per metre cubed (kg/m
Volume (V)
Metres cubed (m3)
Mass (m)
Kilograms (kg)
EDDIE SAYS
You need to be able to match the words to their symbols because this will make it easier for you to find the information needed in an exam. Everyone likes tricks that make answering the question easier, right?!
• Question 4

An object has a mass of 0.1 kg and a volume of 0.4 m3.

Calculate the density of the object.

EDDIE SAYS
This is a simple one if you are able to pick out the numbers and put them into the equation (which is what will be asked of you 90% of the time in the exam!). Let's go through it together: Step 1 Identify the numbers and write them down. ρ = ? m = 0.1 kg V = 0.4 m3 Step 2 Put them into the equation: ρ = 0.1 ÷ 0.4 Step 3 Put this into the calculator and write down your answer. ρ = 0.25 kg/m3
• Question 5

An object has an original density of 1 kg/m3 and is then heated. Its new volume after heating is 0.8 m3.

Calculate the change in density of the object.

Object mass = 2 kg.

EDDIE SAYS
This one is a little more complicated because it has two parts to it. The first part is the simple 'work out the density' part, but then it turns into a 'work out the difference between these two parts' question. Let's have a look at how we would tackle this type of question. Step 1 Work out the density - find the numbers and write them down: ρ = ? m = 2 kg V = 0.8 m3 Put them into the equation: ρ = 2 ÷ 0.8 Do the maths: ρ = 2.5 kg/m3 Step 2 Now take this new value for density away from the original value. 2.5 - 1 = 1.5 kg/m3 It's important not to panic when you get these more complicated questions - just take them one step at a time.
• Question 6

What happens to the density of an object when you cool it?

It increases
EDDIE SAYS
When you cool an object, you are stopping the particles from vibrating as much - this is what heat is - how much particles are vibrating. If the particles are vibrating less, they are taking up less space, this means that the volume of the whole object is going to go down. If you have the same mass in a smaller volume, then your density is going to go up. The correct answer here is increases.
• Question 7

An object is heated.

Describe  and explain what happens to its density by talking about the particles.



EDDIE SAYS
This question has an 'explain' in it - this means you need to have a because in your answer, linking the change in volume to density. Let's have a look in a little more detail. Heating is making the particles vibrate more - heating is all about vibrating those particles. The more the particles vibrate, the more space they will take up. This will increase the volume. That is the description part done - you have stated the facts. Now you need to make a link between the volume and the density. You need to say that because the volume has increased and the mass has not changed, the density will decrease. Great work if you got this one correct!
• Question 8

Describe how to calculate the volume of a cube.



EDDIE SAYS
This question is all about seeing if you can remember how to calculate the volume of a regular object. There are two basic steps that you need to take for this question (you might have guessed this by the two marks). 1 Find the length, width and breadth of an object. Usually by measuring them with a ruler. 2 Multiply them together to get your volume. Boom - done!
• Question 9

Calculate the density of this cube.

Its mass is 0.1 kg. EDDIE SAYS
This question has a few parts and it is the hardest type of question you will get in the foundation paper. Let's look at the steps. Step 1 Work out the volume of the cube. It is a cube, so you are expected to know that all of the sides are the same length. This might be where you make your first mistake - did you convert from cm to m? Each side should be 0.05 m, not 5 m! It should look like this 0.05 x 0.05 x 0.05 = 0.000125 m3 Step 2 Put this into the density equation: ρ = ? m = 0.1 V = 0.000125 ρ = 0.1 ÷ 0.000125 ρ = 800 kg/m3 Well done if you got this one correct!
• Question 10

Put these objects into order with the most dense at the bottom and the least dense at the top.

## Column B

Least dense
Oxygen
In the middle
Ethanol (alcohol)
Most dense
Aluminium
EDDIE SAYS
Did you get it? There was one option from each of the three states of matter! Oxygen (the gas) was the least dense because it is a gas. Then it was ethanol because it is a liquid. Finally, aluminium because it is solid. That's the end of this activity - how do you feel about density now? Hopefully, you are feeling rather more confident than at the beginning! 