# Calculate Density, Mass and Volume

In this worksheet, students will calculate densities, masses and volumes.

Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Derive and Apply Formulae

Difficulty level:

### QUESTION 1 of 10

Density is an example of a compound measure, which is one that involves more than one unit of measurement.

Density is a measure of mass (e.g. kg, g) in relation to unit volume (e.g. m3, cm3) and can be measured in kg/m3, g/cm3 etc.

You should know the following formulae and may use the triangle to help you remember the three Mass, Density, Volume formulae.

Example 1

A large block of oak has a mass of 185 kg and a volume of 0.25 m3

Find its density in kg/m3.

Density = Mass ÷ Volume = 185 ÷ 0.25 = 740  kg/m3.

Example 2

Aluminium has a density of 2.712 g/cm3.  Find the mass of a piece of aluminium with a volume of 12 cm3.

Mass = Density x Volume

Mass = 2.712 x 12 = 32.5 g

Now let's apply these formulae by tackling some questions together!

A piece of chromium has a mass of 50g and a volume of 6.95 cm3.

Find the density of chromium in g/cm3.

(Write your answer to 3 sf and you do not need to include units as they are already given in the question.)

A piece of copper has a mass of ½ kg and a volume of 56 cm3.

Find the density of copper in g/cm3.

(Write your answer to 3 sf and you do not need to include units as they are already given in the question.)

The density of water is 1g/cm3.

Find the mass of 550 cm3 of water in grams.

(Write your answer to 3 sf and you do not need to include units as they are already given in the question.)

The density of iron is 7.85 g/cm3.

Find the volume in cm3 of 500 g of iron.

(Write your answer to 3 sf and you do not need to include units as they are already given in the question.)

The density of gold is 19.32g/cm3.

Find the mass in grams of a piece of gold with volume 50 cm3.

(Write your answer to 3 sf and you do not need to include units as they are already given in the question.)

The density of silver is 10.49 g/cm3.

Find the volume in cm3 of a 300 g piece of silver.

(Write your answer to 3 sf and you do not need to include units as they are already given in the question.)

A piece of platinum has a mass of 192.6 g and a volume of 9 cm3.

Find the density of platinum in g/cm3.

(Write your answer to 3 sf and you do not need to include units as they are already given in the question.)

120 m3 of fuel is poured into the tanks of an aeroplane.  The mass of the aeroplane increases by 88440 kg.

Find the density of the fuel in kg/m3.

(Write your answer to 3 sf and you do not need to include units as they are already given in the question.)

The density of milk is 1.02 g/cm3.

Find the mass in grams of a litre of milk.

(Write your answer to 3 sf and you do not need to include units as they are already given in the question.)

The density of a rock is 11.5 g/cm3 and it has a mass of ½ kg.

Find its volume in cm3.

(Write your answer to 3 sf and you do not need to include units as they are already given in the question.)

• Question 1

A piece of chromium has a mass of 50g and a volume of 6.95 cm3.

Find the density of chromium in g/cm3.

(Write your answer to 3 sf and you do not need to include units as they are already given in the question.)

7.19
EDDIE SAYS
Density = mass / volume Density = 50 g ÷ 6.95 cm³ = 7.19 g/cm³ (3 sf)
• Question 2

A piece of copper has a mass of ½ kg and a volume of 56 cm3.

Find the density of copper in g/cm3.

(Write your answer to 3 sf and you do not need to include units as they are already given in the question.)

8.93
EDDIE SAYS
Density = mass / volume You should know that ½ kg = 500 g 500 g ÷ 56 cm³ = 8.93 g/cm³ How are you getting on?
• Question 3

The density of water is 1g/cm3.

Find the mass of 550 cm3 of water in grams.

(Write your answer to 3 sf and you do not need to include units as they are already given in the question.)

550
EDDIE SAYS
Mass = density x volume Mass = 1 g × 550 cm³ = 550 g/cm³ So really, all you had to do was change the units!
• Question 4

The density of iron is 7.85 g/cm3.

Find the volume in cm3 of 500 g of iron.

(Write your answer to 3 sf and you do not need to include units as they are already given in the question.)

63.7
EDDIE SAYS
Density = mass / volume 500 g ÷ 7.85 cm³ = 63.7 g/cm³ Don't panic if you're still finding these tricky. You can always look back to the introduction and read the explanation again.
• Question 5

The density of gold is 19.32g/cm3.

Find the mass in grams of a piece of gold with volume 50 cm3.

(Write your answer to 3 sf and you do not need to include units as they are already given in the question.)

966
EDDIE SAYS
We know that mass = density x volume So the calculation would be: 19.32 g × 50 cm³ = 966 g/cm³ You've hit halfway, keep pushing.
• Question 6

The density of silver is 10.49 g/cm3.

Find the volume in cm3 of a 300 g piece of silver.

(Write your answer to 3 sf and you do not need to include units as they are already given in the question.)

28.6
EDDIE SAYS
Volume = mass / density 300 g ÷ 10.49 cm³ = 28.6 g Are you feeling more confident?
• Question 7

A piece of platinum has a mass of 192.6 g and a volume of 9 cm3.

Find the density of platinum in g/cm3.

(Write your answer to 3 sf and you do not need to include units as they are already given in the question.)

21.4
EDDIE SAYS
Density = mass / volume 192.6 g ÷ 9 cm³ = 21.4 g/cm³
• Question 8

120 m3 of fuel is poured into the tanks of an aeroplane.  The mass of the aeroplane increases by 88440 kg.

Find the density of the fuel in kg/m3.

(Write your answer to 3 sf and you do not need to include units as they are already given in the question.)

737
EDDIE SAYS
Density = mass / volume 88440 kg ÷ 120 m³ = 737 kg/m³ This question may have seemed more challenging than the previous ones you've completed as it was phrased as a word problem. However, we calculate the equation in the same way. In paper exams it's always useful to have a highlighter handy in order to underline key information in the question.
• Question 9

The density of milk is 1.02 g/cm3.

Find the mass in grams of a litre of milk.

(Write your answer to 3 sf and you do not need to include units as they are already given in the question.)

1020
EDDIE SAYS
You know that there are 1000 grams in a litre. So, you needed to times the density given by 1000 in order to find the density of a litre of milk. 1.02 g/cm³ × 1000 = 1020 g/cm³ Hopefully this question didn't catch you out! Always read the word problem carefully in order to find our exactly what is being asked of you.
• Question 10

The density of a rock is 11.5 g/cm3 and it has a mass of ½ kg.

Find its volume in cm3.

(Write your answer to 3 sf and you do not need to include units as they are already given in the question.)

43.5
EDDIE SAYS
We know that ½ kilo = 500 g We also know that volume = mass / density So we need to calculate 500 g ÷ 11.5 g/cm³ = 43.5 cm³ Great focus, that's another activity ticked off!
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