The smart way to improve grades

Comprehensive & curriculum aligned

Try an activity or get started for free

Find Mass, Density and Volume

In this worksheet, students will practise using the Mass, Density, Volume formulae pyramid to identify the correct single formula to apply to find a missing metric.

Worksheet Overview

QUESTION 1 of 10

While speed, distance and time are the most common compound units you will encounter in exams, you still need to be able to find others too.

In this activity, we will be focusing on here is density, mass and volume.

 

Density is a measurement of how heavy something is for a given unit of mass; (effectively, the denser an object is, the heavier it is.)

 

The most challenging element of calculating with density, mass and volume is in remembering the formulae you will need to apply. 

 

How to Remember the Formulae

The easiest approach is to memorise the formulae triangle shown below, which we can then use to find the single formula we need to apply:

 

 

 

How We Use this Formulae Triangle

It's quite simple, just highlight the element you are trying to find (we've done it below with a red circle) and the formula to find this will use the elements which are left over:

 

 

Let's look at these formulae in action now in some examples. 

 

 

e.g. Find the volume of an object that has a density of 20 g/cm3 and a mass of 500 g.

 

The first step in these calculations is always to decide which element we are trying to find.

For this question, we are directly asked for the volume, so we need to use:

V = M ÷ D

 

Now we can simply plug our numbers into this formula: 

V = 500 ÷ 20

 

The last question that we need to ask ourselves is what units of measurement we need to use.

The trick here is that they are always the same as one of the units provided in the question.

The density here is given in g/cm3, so our volume must be cm3.

 

So Distance = 25 cm3

 

 

 

e.g. An object has a volume of 75 cm3 and a mass of 15 g. Find the average density of the object.

 

Once again, we need to decide which formula.

Don't worry that it asks for average density here, we can still use the same formula:

D = M ÷ V

 

Plugging in our numbers gives us: 

D = 15 ÷ 75 = 0.2

 

Our units are grams per cm3 (remember, the units always are in the question).

 

So Density = 0.2 g/cm3

In this activity, we will use the Mass, Density, Volume formulae pyramid to identify the correct single formula to apply to find a missing metric using the method demonstrated above. 

Type two words in the spaces to complete the sentence below. 

An object has a mass of 7 kg and a volume of 2 cm3.

 

What is the average density of this object? 

14 kg/cm3

3.5 kg/cm3

9 kg/cm3

Find the average density of an object with a mass of 9 g and a volume of 3 cm3.

 

Type your answer as a number without a unit in the box below, as this has already been provided for you. 

14 kg/cm3

3.5 kg/cm3

9 kg/cm3

Type two words in the spaces to complete the sentence below. 

14 kg/cm3

3.5 kg/cm3

9 kg/cm3

A metal bar has a density of 10 g/cm3 and a volume of 2 cm3.

 

What is the mass of this metal bar? 

5 g

20 g

What is the mass of an object that has a density of 4 kg/m3 and a volume of 3 m3?

 

Type your answer as a number without a unit in the box below, as this has already been provided for you. 

5 g

20 g

Type two words in the spaces to complete the sentence below. 

5 g

20 g

A 10 kg box has an average density of 4 kg/m3.

 

What is the volume of this box?

40 m3

2.5 m3

What is the mass of a 4 kg box has an average density of 10 kg/m3

 

Type your answer as a number without a unit in the box below, as this has already been provided for you. 

40 m3

2.5 m3

Match each volume on the left with its corresponding mass and density on the right. 

Column A

Column B

4 m3
25 kg; 10 kg/m3
2.5 m3
3 kg; 0.5 kg/m3
6 m3
40 kg; 10 kg/m3
1.2 m3
12 kg; 10 kg/m3
  • Question 1

Type two words in the spaces to complete the sentence below. 

CORRECT ANSWER
EDDIE SAYS
Remember that we need to look at our formulae pyramid and cover up the variable we are seeking. If we cover Density, then we are left with: Density = Mass ÷ Volume As with any division sum, it is essential to get these two elements the right way round or we will not reach the correct answer.
  • Question 2

An object has a mass of 7 kg and a volume of 2 cm3.

 

What is the average density of this object? 

CORRECT ANSWER
3.5 kg/cm3
EDDIE SAYS
It's all about identifying the correct formula to use in these cases. We are looking for density so if we cover this in our pyramid, we are left with the formula: Density = Mass ÷ Volume Now we just need to substitute our values into this formula: Density = 7 ÷ 2 Density = 3.5 kg/cm3
  • Question 3

Find the average density of an object with a mass of 9 g and a volume of 3 cm3.

 

Type your answer as a number without a unit in the box below, as this has already been provided for you. 

CORRECT ANSWER
EDDIE SAYS
We are seeking the density again here, so we need to use the same formula as the previous question: Density = Mass ÷ Volume Now we just need to substitute our values into this formula: Density = 9 ÷ 3 Density = 3 g/cm3
  • Question 4

Type two words in the spaces to complete the sentence below. 

CORRECT ANSWER
EDDIE SAYS
Remember that we need to look at our formulae pyramid and cover up the variable we are seeking. If we cover Mass, then we are left with: Mass = Density × Volume As with any multiplication sum, we can mix the order of these elements if we choose, so calculating 'Density × Volume' or 'Volume × Density' will give the same answer.
  • Question 5

A metal bar has a density of 10 g/cm3 and a volume of 2 cm3.

 

What is the mass of this metal bar? 

CORRECT ANSWER
20 g
EDDIE SAYS
It's all about identifying the correct formula to use in these cases. We are looking for mass so if we cover this in our pyramid, we are left with the formula: Mass = Density × Volume Now we just need to substitute our values into this formula: Mass = 10 × 2 Mass = 20 g
  • Question 6

What is the mass of an object that has a density of 4 kg/m3 and a volume of 3 m3?

 

Type your answer as a number without a unit in the box below, as this has already been provided for you. 

CORRECT ANSWER
EDDIE SAYS
We are seeking the mass again here, so we need to use the same formula as the previous question: Mass = Density × Volume Now we just need to substitute our values into this formula: Mass = 4 × 3 Mass = 12 kg
  • Question 7

Type two words in the spaces to complete the sentence below. 

CORRECT ANSWER
EDDIE SAYS
Remember that we need to look at our formulae pyramid and cover up the variable we are seeking. If we cover Volume, then we are left with: Volume = Mass ÷ Density As with any division sum, it is essential to get these two elements the right way round or we will not reach the correct answer.
  • Question 8

A 10 kg box has an average density of 4 kg/m3.

 

What is the volume of this box?

CORRECT ANSWER
2.5 m3
EDDIE SAYS
It's all about identifying the correct formula to use in these cases. We are looking for volume so if we cover this in our pyramid, we are left with the formula: Volume = Mass ÷ Density Even though the '10 kg' is not explicitly flagged as the mass, we know that it must be, by a process of elimination, as it is the only value which has not been assigned. Now we just need to substitute our values into this formula: Volume = 10 ÷ 4 Volume = 2.5 m
  • Question 9

What is the mass of a 4 kg box has an average density of 10 kg/m3

 

Type your answer as a number without a unit in the box below, as this has already been provided for you. 

CORRECT ANSWER
EDDIE SAYS
We are seeking the volume again here, so we need to use the same formula as the previous question: Volume = Mass ÷ Volume Now we just need to substitute our values into this formula: Volume = 4 ÷ 10 Volume = 0.4 m3
  • Question 10

Match each volume on the left with its corresponding mass and density on the right. 

CORRECT ANSWER

Column A

Column B

4 m3
40 kg; 10 kg/m3
2.5 m3
25 kg; 10 kg/m3
6 m3
3 kg; 0.5 kg/m3
1.2 m3
12 kg; 10 kg/m3
EDDIE SAYS
All of these calculations are seeking volume so we need to apply the same formula in each case: Volume = Mass ÷ Volume Work with the pairs of info on the right first, then match each to its correct volume. Volume = 40 ÷ 10 = 4 m3 Volume = 25 ÷ 10 = 2.5 m3 Volume = 3 ÷ 0.5 = 6 m3 Volume = 12 ÷ 10 = 1.2 m3 The one that may have caught you out is dividing by 0.5. Remember that dividing by 0.5 is exactly the same as multiplying by 2. You can now use the Mass, Density, Volume formulae pyramid to identify the single formula to use to find a missing variable, and then apply this.
---- OR ----

Get started for free so you can track and measure your child's progress on this activity.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started
laptop

Try an activity or get started for free