Nets and Surface Area

Nets and Surface Area


Nets and Surface Area

A net is a deconstructed 3D shape folded out flat. Nets can be helpful when we want to calculate the surface area of a 3D shape.

Skill 1: Nets of Cubes

A net shows us each face of a shape when it is laid out flat, and there are often many different nets for a 3D shape. Below are some examples of nets of cubes.

Note: these are only some of the nets of a cube – there are many more

Each of the nets above can be folded up to construct a cube, like so:

cube construction from a net

Cubes are the simplest nets you will encounter, so make sure you are comfortable drawing them before moving on to harder shapes.

Level 1-3KS3AQAEdexcelOCRWJEC

Skill 2: Nets of Other Shapes

There are some other common shapes that you should familiarise yourself with, including prisms and pyramids.

A prism is like a 2D shape ‘stretched out’ with the original 2D at either end. This makes drawing a net of a prism fairly simple, as it will feature the 2D shape at both ends with rectangles between them that form the ‘stretched out’ section. A cuboid is also a type of prism, so the net of a cuboid follows the same pattern.

A pyramid always features a 2D shape as its base, with each edge linked to a triangular face. These triangular faces all converge to a central point above the centre of the base. The nets of pyramids are easy to draw – just draw the shape of the base with triangles attached to each side.

A cylinder can be thought of as a circular prism. Its net follows the same pattern as the nets of prisms.

Some examples of nets of 3D shapes are shown below:

nets of 3D shapesLevel 1-3KS3AQAEdexcelOCRWJEC

Skill 3: Finding the Surface Area

We can use nets to find the surface area of a 3D shape – the combined area of all the faces.

Consider the following net of a cuboid.

surface area of a cuboid

We can use the net to work out the surface area. There are 3 ‘pairs’ of faces that are the same – if we calculate the areas of these individual faces we can add them all up to get the surface area of the cuboid.

cuboid surface area nets

The total surface area is therefore:

2 \times48 + 2 \times32 + 2 \times 24  = 208 cm^2

Note: remember that the units of area are cm^2, m^2 etc.


Level 1-3KS3AQAEdexcelOCRWJEC

Example 1: Surface Area of a Cylinder

Calculate the surface area of cylinder A from the net shown.

[3 marks]


cylinder net surface area

The diameter of the circular face is 6 cm, meaning the radius of the circle is 3 cm. We can calculate the area of one circular face using the formula:

Area of a circle = \pi r^2

So the area of both circular faces on the cylinder is:

2\times \pi \times 3^2=18\pi = 56.55 cm^2

To calculate the area of the rectangle, we need to know the length – this is the same as the circumference of the circle (2\pi r).



cylinder net surface area
cylinder net surface area

The length of the rectangle is therefore:

2\pi r = 6 \pi cm

We can now calculate the area of the rectangle face:

6 \pi \times 6 = 36 \pi = 113.10 cm^2

The total surface area of the cylinder is therefore:

\text{Area} = 56.55 + 113.10=169.65 cm^2



Level 4-5KS3AQAEdexcelOCRWJEC


There is a simple formula for calculating the surface area of a cylinder:

Surface area of a cylinder =2\pi rh + 2\pi r^2

Where r is the radius of the circle face and h is the height of the cylinder.

Substituting values into this formula is a quick way of performing the calculations shown in the example above.

Example Questions

Only nets A and C will form a cube.

The faces on net B will overlap when folded over and net D has too many faces.

Your completed sketch should look something like this:


We need to use the following formula:

Area of a triangle =\dfrac{1}{2} \times \text{base} \times \text{height}

So the area of both triangular faces is:


2\times \dfrac{1}{2}\times4\times3 = 12 cm^2


The area of the three rectangular faces is:


3\times10\times4 = 120 cm^2


The total surface area is:

12+120=132 cm^2

Use the formula and substitute in the values of r=2 and h= 8:


\begin{aligned}\text{Surface area} &= 2\pi r^2 + 2\pi rh \\  &=(2 \times \pi \times 2^2) + (2\times \pi \times 2 \times 8) \\ &= 8\pi + 32\pi \\ &= 25.13+100.53\\ &=125.66 \text{ cm}^2\end{aligned}

The surface area of the pyramid is given by:


\text{Surface area}= 4\times \text{area of triangle }+ \text{area of square base}


Use the formula for the area of the triangle:


\text{Area of a triangle}=\dfrac{1}{2} \times \text{base} \times \text{height}


Substitute in the values from the net (base =4 cm and height =9 cm) to calculate the area:


\begin{aligned}\text{Surface area} &= (4\times \dfrac{1}{2}\times4\times9) + (4\times4) \\[1.5em] &= 72+16 \\[1.5em] &= 88 \text{ cm}^2 \end{aligned}

You May Also Like...

KS3 Maths Worksheets

KS3 Maths Worksheets are an excellent way for KS3 students to prepare and practice for final term exams. They will ensure students have a sufficient base knowledge before going into KS4 and studying for their GCSEs.

View Product

KS3 Maths Practice Papers

KS3 practice papers are perfect for preparing students for their KS3 maths tests and end of year exams. Order today and get the exam pack delivered to your door.

From: £4.99
View Product

KS3 Maths Revision Cards

Whether you are buying these maths cards for a year 7 student who loves maths and wants to learn more or you are getting them for a reluctant year 9 student who has an end of year exam, these cards will be useful. Our KS3 maths revision cards are effective and will help to engage your child with their maths revision.

View Product

GCSE Maths Revision Cards

Revise for your GCSE maths exam using the most comprehensive maths revision cards available. These GCSE Maths revision cards are relevant for all major exam boards including AQA, OCR, Edexcel and WJEC.

View Product

GCSE Maths Revision Guide

The MME GCSE maths revision guide covers the entire GCSE maths course with easy to understand examples, explanations and plenty of exam style questions. We also provide a separate answer book to make checking your answers easier!

From: £14.99
View Product

GCSE Maths Predicted Papers 2022 (Advance Information)

GCSE Maths 2022 Predicted Papers are perfect for preparing for your 2022 Maths exams. These papers have been designed based on the new topic lists (Advance Information) released by exam boards in February 2022! They are only available on MME!

From: £5.99
View Product