Nets and Surface Area (2025)

Nets and Surface Area Revision

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.

Nets and Surface Area (1)

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:

Nets and Surface Area (2)

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

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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:

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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.

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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.

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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.

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Example: Surface Area of a Cylinder

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

[3 marks]

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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).

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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

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Note:

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.

Nets and Surface Area Example Questions

Only netsA andC will form a cube.

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

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Your completed sketch should look something like this:

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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

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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}

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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}

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Nets and Surface Area (2025)

FAQs

Nets and Surface Area? ›

A net is a 2-dimensional shape that can be folded to form a 3-dimensional shape or solid, showing each face and edge of the figure in 2-dimensions. Nets are helpful for finding the surface area of solids, which is the measure of the total area of all its faces.

How to find surface area using net? ›

The formula for any other shape is break into other shapes (triangles, squares, etc.), find the area for all the broken-up shapes, and add it all up. Once you have found the area for all the parts of the net, add the parts together to find the area of a net.

How can nets be used to find area? ›

To find the surface area of a prism, it can be helpful to sketch the net, find the area of each shape in the net, and then add the areas together. To find the surface area of this triangular prism, find the area of the three rectangles and two triangles in its net and add all the areas together.

What is the surface area of the prism net? ›

Any prism is given by SA = PH +2B where P is the perimeter of the base (in a rectangular prism, you could choose any side as one of the bases), H is the height of the prism (the third dimension apart from the length and width of the base) and B is the area of the base.

How is the formula for the surface area of a cylinder related to the net of the cylinder? ›

The net of the cylinder can, therefore, be drawn out as follows. To find the surface area of the cylinder, we need to work out the area of its net. The area of each of the circles is 𝜋 𝑟  , and the area of the rectangle is calculated by multiplying its length and width to get ℎ × 2 𝜋 𝑟 = 2 𝜋 𝑟 ℎ .

Is surface area and net the same thing? ›

Surface Area using a Net: Surface area is the sum of the areas of all of the polygonal faces of a solid. Surface area is labeled in " square units". A "net" is a two-dimensional shape that can be folded to form a three dimensional shape or solid.

How do I calculate surface area? ›

Surface area is total area on the surface of a three-dimensional shape. To find the surface area of a cuboid which has 6 rectangular faces, add the areas of all 6 faces. Or, you can label the length (l), width (w), and height (h) of the cuboid and use the formula: surface area (SA)=2lw+2lh+2hw.

What are nets used for in math? ›

The 'net' of a shape (also called a geometry net) is a term used to describe what a 3D shape would look like if it was opened out and laid flat. A net of a simple symmetrical shape such as the cube may have different patterns but will end up with just one unique shape. A cube has 11 nets or patterns.

How can you use a net to find the surface area of a polyhedron? ›

The surface area of a polyhedron is the sum of the areas of all of the faces. Because a net shows us all faces of a polyhedron at once, it can help us find the surface area. We can find the areas of all polygons in the net and add them. A square pyramid has a square and four triangles for its faces.

How do nets work? ›

Fish are caught in gillnets or entanglement nets in one of three ways: gilled—the fish tries to swim through one or more meshes; if it cannot pass through, it becomes caught behind its gill covers as it tries to back out of the net. wedged—the fish is tightly held in the net around the body by one or more meshes.

How to find the net of a figure? ›

Step 1: Identify the given solid figure. Step 2: Identify the faces and side lengths of the given solid figure. Step 3: Using the side lengths and shape of the faces, draw each face of the solid figure on a plane and mark the corresponding side length. You will get the net of the solid figure.

What is the surface area of a net cube? ›

Surface area of cube is the sum of areas of all the faces of cube, that covers it. The formula for surface area is equal to six times of square of length of the sides of cube. It is represented by 6a2, where a is the side length of cube.It is basically the total surface area. Also, learn Volume Of A Cube.

What is a net for a cylinder? ›

The net of a cylinder looks like a rectangle with two circles attached at opposite ends. We also define a base radius for the cylinder as the radius of the base, and the height of the cylinder as the distance between the bases.

How to find the surface area of a prism? ›

To find the surface area of a prism, use the formula SA=2B+ph, where SA stands for surface area, B stands for the area of the base of the prism, p stands for the perimeter of the base, and h stands for height of the prism. Since this is a rectangular prism, substitute the area formula of a rectangle for B.

What is the formula to find the total surface area? ›

Surface Area and Volume Formulas
NamePerimeterTotal Surface Area
Circle2 π rπ r2
Ellipse2π√(a2 + b2)/2π a.b
Trianglea+b+c1/2 * b * h
Cuboid4(l+b+h)2(lb+bh+hl)
9 more rows

How do you calculate net wall area? ›

To calculate the area of a wall, use the standard formula of Length x Width = Area. Next, use the same formula to record the individual area of windows and doors.

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