Surface Area Of A Cube

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

There are also surface area 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 surface area of a cube?

The surface area of a cube is the sum of the areas of all the faces of a cube. A cube is a three-dimensional solid object that has six congruent square faces. This means they are all the same size.

To find the area of each face we multiply the side lengths together. We then multiply the area of each of the square faces by six.

The formula to calculate the surface area, S, of a cube is

S=6x^{2}

where x represents the side length of the cube.

We can use this formula to find the surface area of any cube.

Surface Area Of A Cube Image 1

Surface area is measured in square units, for example mm^{2}, \ cm^{2} or m^{2}.

What is the surface area of a cube?

What is the surface area of a cube?

How to calculate the surface area of a cube

In order to calculate the surface area of a cube:

  1. Write the formula for the surface area of the cube.
  2. Substitute any known value(s) into the formula.
  3. Complete the calculation.
  4. Write the solution, including the units.

Explain how to calculate the surface area of a cube

Explain how to calculate the surface area of a cube

Volume and surface area of a cube worksheet

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

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Volume and surface area of a cube worksheet

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

COMING SOON

Surface area of a cube examples

Example 1: integer side lengths

Work out the surface area of the cube below.

Surface Area Of A Cube example 1

  1. Write the formula for the surface area of the cube.

S=6x^{2}

2Substitute any known value(s) into the formula.

Here, x=5 and so we have

S=6\times{5}^{2}.

3Complete the calculation.

S=6\times{5}^{2}=6\times{25}=150

4Write the solution, including the units.

As the unit of length is centimetres (cm), the unit of area is square centimetres (cm^{2}).

S=150cm^{2}.

Example 2: one known edge of the cube

Work out the surface area of the cube.

Surface Area Of A Cube example 2

S=6x^{2}

Substituting x=6 into the formula, we have


S=6\times{6}^{2}.

S=6\times{6}^{2}=6\times{36}=216

As the unit of length is centimetres (cm), the unit of area is square centimetres (cm^{2}).


S=216cm^{2}

Example 3: worded problem

A cube structure has a side length of 7m. Calculate the total surface area of the structure.

S=6x^{2}

Substituting x=7 into the formula, we have


S=6\times{7}^{2}.

S=6\times{7}^{2}=6\times{49}=294

As the unit of length is metres (m), the unit of area is square metres (m^{2}).


S=294m^{2}

Example 4: area of a face given

The area of the face of a cube is 30cm^{2}. Work out the surface area of the cube.

S=6x^{2}

As we know the area of one face of the cube, we can express this as x^{2}=30 as x is the side length of the cube, and we know the area, x^{2}.


Substituting x^{2}=30 into the formula, we have


S=6\times{30}.

S=6\times{30}=180

As the unit of area is square centimetres (cm^{2}), we can use this in the solution.


S=180cm^{2}

Example 5: find the length of a cube given the surface area

The surface area of a cube is 24cm^{2}. Work out the length of the cube.

S=6x^{2}

Here we know that S=24 and so substituting this into the formula, we have


24=6\times{x}^{2}.

Dividing both sides by 6, we have


\begin{aligned} 24\div{6}&=x^{2}\\\\ 4&=x^{2} \\\\ x&=2 \end{aligned}

As the unit of area is square centimetres (cm^{2}), the unit length will be in centimetres.


x=2cm

Example 6: find the length of a cube given the surface area (decimal solution)

The surface area of a cube is 483mm^{2}. Work out the length of the side x correct to 2 decimal places.

Surface Area Of A Cube example 6

S=6x^{2}

As we know the surface area, we can substitute S=483 into the formula


483=6\times{x}^{2}.

To complete the calculation, we need to divide both sides by 6 first, and then square root both sides to find x.


\begin{aligned} 483\div{6}&=x^{2}\\\\ 80.5&=x^{2}\\\\ \sqrt{80.5}&=x\\\\ x&=8.972179222463… \end{aligned}

x=8.97mm \ (2dp).

Common misconceptions

  • Missing/incorrect units

You should always include units in your answer.

Surface area is measured in square units (for example, mm^2, \ cm^2, \ m^2 etc.).

  • Calculating with different units

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

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

  • Calculating volume instead of surface area

Volume and surface area are different quantities. The volume of the cube is the three-dimensional space in a shape and is measured in cubic units.

Surface area is the amount of space covering the outside of a 3D shape. To find surface area, we need to work out the area of one face and multiply it by six. 

Practice surface area of a cube questions

1. Work out the surface area of the cube.

 

Surface Area Of A Cube Practice Question 1

27cm^3
GCSE Quiz False

12cm^2
GCSE Quiz False

36cm^2
GCSE Quiz False

54cm^2
GCSE Quiz True

S=6x^{2} where x=3cm.

 

S=6\times{3}^{2}=6\times{9}=54cm^{2}.

2. Calculate the surface area of the cube below. Write your answer in square centimetres.

 

Surface Area Of A Cube Practice Question 2

0.125cm^3
GCSE Quiz False

15,000cm^2
GCSE Quiz True

6cm^2
GCSE Quiz False

1.5cm^2
GCSE Quiz False

S=6x^{2} where x=0.5m = 50cm.

 

S=6\times{50}^{2}=6\times{2500}=15,000cm^{2}.

3. Work out the surface area of the cube. Give your answer in cm^{2}.

 

Surface Area Of A Cube Practice Question 3

96cm^2
GCSE Quiz False

9,600cm^2
GCSE Quiz True

960cm^2
GCSE Quiz False

9.6cm^2
GCSE Quiz False

S=6x^{2} where x=40cm=0.4m.

 

S=6\times{40}^{2}=6\times{1600}=9,600cm^{2}.

4. The surface area of a cube is 150cm^{2}. Find the length of the side of the cube.

135 \ 000cm
GCSE Quiz False

2.04cm
GCSE Quiz False

5cm
GCSE Quiz True

12.5cm
GCSE Quiz False

S=6x^{2} where S=150cm^{2}.

 

\begin{aligned} 150&=6\times{x}^{2}\\\\ 25&=x^{2}\\\\ x&=\sqrt{25}\\\\ x&=5 \end{aligned}

5. The surface area of a cube is 6m^{2}. Work out the length of each side x.

 

Surface Area Of A Cube Practice Question 5

2m
GCSE Quiz False

1m
GCSE Quiz True

0.3m
GCSE Quiz False

0.41m
GCSE Quiz False

S=6x^{2} where S=6m^{2}.

 

\begin{aligned} 6&=6\times{x}^{2}\\\\ 6\div{6}&=x^{2}\\\\ x^{2}&=1\\\\ x&=\sqrt{1}\\\\ x&=1 \end{aligned}

6. The surface area of a cube is 186m^{2}. Work out the length of each side. Write your answer to the nearest centimetre.

5.57m
GCSE Quiz True

2.27m
GCSE Quiz False

15.50m
GCSE Quiz False

207,576m
GCSE Quiz False

S=6x^{2} where S=186m^{2}.

 

\begin{aligned} 186&=6\times{x}^{2}\\\\ 31&=x^{2} \\\\ x&=\sqrt{31}=5.567764362830…=5.57\text{ (2dp)} \end{aligned}

Surface area of a cube GCSE questions

1. Here is a cube.

 

Surface Area Of A Cube GCSE Question 1

 

The cube has a volume of 216cm^{3}.

Given that V=x^{3}, where x is the side length of the cube, work out the total surface area of the cube.

 

(4 marks)

Show answer
x=\sqrt[3]{216} \ (=6cm)

(1)

6 \times 6 \ or \ 36cm^2

(1)

6 \times 6 \times 6 \ or \ 36 \times 6

(1)

216cm^2

(1)

2. The diagram shows a cube of side 3cm.

 

Surface Area Of A Cube GCSE Question 2

 

Determine the volume : surface area ratio of the cube.

Write your answer as a ratio in the simplest form.

 

(5 marks)

Show answer

3 \times 3 \times 6 \ or \ 9 \times 6

(1)

54cm^2

(1)

3 \times 3 \times 3 = 27cm^3

(1)

27:54

(1)

1:2

(1)

3. The total surface area of a cube is 294cm^{2}. Work out the side length of the cube.

 

(3 marks)

Show answer

294 \div{6} \ or \ 49

(1)

\sqrt{49}

(1)

7cm

(1)

Learning checklist

You have now learned how to:

  • Calculate the surface area of a cube
  • 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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