Volume of a cube

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In order to access this I need to be confident with:

3D shapes Area of a quadrilateral Substitution

This topic is relevant for:

GCSE Maths Geometry and Measure 3D Shapes Cuboid

Volume Of A Cube

Here we will learn about the volume of a cube, including how to calculate the volume of a cube and how to find missing lengths of a cube given its volume.

There are also volume of a cube worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is the volume of a cube?

The volume of a cube is the amount of space there is within a cube.

A cube is a three-dimensional shape with $6$ square faces.

To find the volume of a cube, with side length $a,$ we can use the volume of a cube formula,

\text {Volume }=a^{3}.

Volume is measured in cubic units for example, $mm^{3}, \ cm^{3}$ or $m^{3}.$

For example,

The volume of this cube is

\begin{aligned} \text{Volume} &=a^{3} \\\\ \text{Volume} &=8^{3} \\\\ \text{Volume} &=512 \mathrm{~cm}^{3} \end{aligned}

What is the volume of a cube?

How to calculate the volume of a cube

In order to calculate the volume of a cube:

Write down the formula.

$\text{Volume }=a^{3}$
Substitute the values into the formula.
Work out the calculation.
Write the answer and include the units.

Explain how to calculate the volume of a cube

Volume and surface area of a cube worksheet

Get your free volume and surface area of a cube worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Volume and surface area of a cube worksheet

Get your free volume and surface area of a cube worksheet of 20+ questions and answers. Includes reasoning and applied questions.

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Volume of a cube examples

Example 1: volume of a cube

Work out the volume of the cube.

Write down the formula.

\text{Volume }=a^{3}

2Substitute the values into the formula.

Here the sides of the cube are $6cm.$

\text{Volume }=6^{3}

3Work out the calculation.

\begin{aligned} \text{Volume} &=6 \times 6 \times 6\\\\ &=216 \end{aligned}

4Write the answer and include the units.

The measurements are in $cm$ therefore the volume will be in $cm^{3}.$

\text{Volume }=216 \mathrm{~cm}^{3}

Example 2: volume of a cube

Work out the volume of this cube.

Write down the formula.

\text{Volume }=a^{3}

Substitute the values into the formula.

Here the edges are $7cm.$

$\text{Volume }=7^{3}$

Work out the calculation.

\begin{aligned} \text{Volume} &=7 \times 7 \times 7\\\\ &=343 \end{aligned}

Write the answer and include the units.

The measurements are in cm therefore the volume will be in $cm^{3}.$

$\text{Volume }=343 \mathrm{~cm}^{3}$

Example 3: volume of a cube – different units

Work out the volume of this cube.

Write down the formula.

\text{Volume }=a^{3}

Substitute the values into the formula.

Notice here that one of the units is in $cm$ whilst the other is in $m.$ We need all the units to be the same to calculate the volume. This is a cube so we know all the edges are the same length, so we can easily change $m$ to $cm, \ 0.6 \ m = 60 \ cm.$

$\text{Volume }=60^{3}$

Work out the calculation.

\begin{aligned} \text {Volume }&=60 \times 60 \times 60 \\\\ &=216000 \end{aligned}

Write the answer and include the units.

The measurements are in cm therefore the volume will be in $cm^{3}.$

$\text{Volume }=216000 \mathrm{~cm}^{3}$

How to work out a missing length given the volume

Sometimes we are given the volume of a cube and need to work out the length of an edge.

We can do this by substituting the volume into the formula for the volume of a cube and then solving the equation that is formed. This will give us the length of the sides of a cube.

Write down the formula.
$\text{Volume }=a^{3}$
Substitute the values that you do know into the formula.
Solve the equation.
Write the answer and include the units.

Finding the length given the volume examples

Example 4: find the length of a cube given the volume

The volume of the cube is $64 \ cm^{3}.$ Work out the length of the cube.

Write down the formula.

\text{Volume }=a^{3}

Substitute the values that you do know into the formula.

a^{3}=64

Solve the equation.

\begin{aligned} a^{3}&=64 \\\\ a&=\sqrt[3]{64} \\\\ a&=4 \end{aligned}

Write the answer and include the units.

Since the measurement for the volume in this question was in $cm^{3},$ the length will be in $cm.$

$a=4 \ \mathrm{~cm}$

Example 5: find the length of a cube given the volume

The volume of the cube is $1000 \ m^{3}.$ Work out the length of each side, $x.$

Write down the formula.

\text{Volume }=x^{3}

Substitute the values that you do know into the formula.

x^{3}=1000

Solve the equation.

\begin{aligned} x^{3}&=1000 \\\\ x&=\sqrt[3]{1000} \\\\ x&=10 \end{aligned}

Write the answer and include the units.

Since the measurement for the volume in this question was in $m^{3},$ the length will be in $m.$

$x=10 \ \mathrm{~m}$

Common misconceptions

Missing/incorrect units

You should always include units in your answer.

Volume is measured in units cubed (e.g. $mm^{3}, \ cm^{3}, \ m^3$ etc).

Calculating with different units

You need to make sure all measurements are in the same units before calculating volume.

For example, you can’t have some in $cm$ and some in $m.$

Dividing by three rather than cube rooting

If you are given the volume of a cube and you need to find the side length, remember the inverse of cube is cube root, not divide by $3.$

For example, if the volume of a cube is $27 \ cm^{3},$ the side length is $\sqrt[3]{27}=3 \ \mathrm{cm}$ (not $27 \div 3$ ).

Surface area of a cuboid is part of our series of lessons to support revision on cuboid. You may find it helpful to start with the main cuboid lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

Practice volume of a cube questions

9 \ \mathrm{cm}^{3}

27 \ \mathrm{cm}^{3}

54 \ \mathrm{cm}^{3}

36 \ \mathrm{cm}^{3}

\begin{aligned} \text{Volume } &=a^{3} \\\\ \text{Volume } &=3^{3} \\\\ &=3 \times 3 \times 3 \\\\ &=27 \mathrm{~cm}^{3} \end{aligned}

1.25 \ \mathrm{m}^{3}

150 \ \mathrm{m}^{3}

125 \ \mathrm{m}^{3}

0.125 \ \mathrm{m}^{3}

\begin{aligned} \text{Volume }&=a^{3}\\\\ \text{Volume }&=0.5^{3}\\\\ &=0.5 \times 0.5 \times 0.5\\\\ &=0.125 \mathrm{~m}^{3} \end{aligned}

64000 \ \mathrm{cm}^{3}

96 \ \mathrm{cm}^{3}

64 \ \mathrm{cm}^{3}

6.4 \ \mathrm{m}^{3}

Notice here that one of the units is in $cm$ whilst the other is in $m$ . We need all the units to be the same to calculate the volume.

This is a cube, we know all the edges are the same length, so we can easily change $m$ to $cm, \ 0.4 \ m = 40 \ cm.$

\begin{aligned} \text{Volume }&=a^{3}\\\\ \text{Volume }&=40^{3}\\\\ &=40 \times 40 \times 40\\\\ &=64000 \end{aligned}

The measurements are in $cm$ therefore the volume will be in $cm^{3}.$

\text{Volume }=64000 \ \mathrm{~cm}^{3}

7 \ \mathrm{cm}^{3}

114.3 \ \mathrm{~cm}

7 \ \mathrm{~cm}

114.3 \ \mathrm{m}^{3}

\text{Volume }=a^{3}

\begin{aligned} a^{3}&=343 \\\\ a&=\sqrt[3]{343} \\\\ a&=7 \mathrm{~cm} \end{aligned}

5 \ \mathrm{~m}

41.6 \ \mathrm{m}^{3}

41.6 \ \mathrm{~m}

5 \ \mathrm{m}^{3}

\text{Volume }=x^{3}

\begin{aligned} x^{3}&=125 \\\\ x&=\sqrt[3]{125} \\\\ x&=5 \mathrm{~m} \end{aligned}

4 \ \mathrm{~m}

21.3 \ \mathrm{m}^{3}

21.3 \ \mathrm{~m}

400 \ \mathrm{~cm}

\text{Volume }=a^{3}

\begin{aligned} a^{3}&=64 \\\\ a&=\sqrt[3]{64} \\\\ a&=4 \mathrm{~m} \end{aligned}

4m = 400 \ cm

a=400 \mathrm{~cm}

Volume of a cube GCSE questions

1. Here is a cube.

Volume of a cube gcse question 1

Work out the volume of the cube.

(2 marks)

Show answer

\text{Volume}=2 \times 2 \times 2

(1)

\text{Volume}=8 \ \mathrm{m}^{3}

(1)

2. (a) This sculpture is formed by placing one cube on top of another. Work out the total volume of the sculpture.

Volume of a cube gcse question 2

(b) The density of the material used to make the sculpture is $2.7 \ g/cm^{3}.$ Work out the total mass of the sculpture. Give your answer in $kg,$ to the nearest $kg.$

You may use $\text{density }= \frac{\text{mass}}{\text{volume}}$ .

(5 marks)

Show answer

(a)

Volume of bottom cube $= 60 \times 60 \times 60=216000 \ cm^3$

(1)

Volume of top cube $= 35 \times 35 \times 35=42875 \ cm^3$

(1)

Total volume $= 216000+42875=258875 \ cm^3$

(1)

(b)

2.7=\frac{m}{258875}

(1)

2.7 \times 258875=698962.5 \ \mathrm{g}

(1)

$698962.5 \ g=698.9625 \ kg=699 \ kg$ (nearest $kg$ )

(1)

3. A cube has a volume of $343 \ m^{3}.$ Find the length of the cube. Give your answer in $cm.$

(3 marks)

Show answer

$x^{3}=343$ or $x=\sqrt[3]{343}$

(1)

x= 7 \ m

(1)

x= 700 \ cm

(1)

Learning checklist

You have now learned how to:

Understand and apply the formula to calculate the volume of cubes

Use the properties of faces, surfaces, edges and vertices of cubes and cuboids to solve problems in 3D

The next lessons are

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