Surface area of cubes and cuboids

Part ofMathsPerimeter, Area, Volume

Key points

A series of five images. Each image shows the same cube. The first image shows a cabinet projection of a cube. The top and base faces are coloured orange. The second image shows a cabinet projection of a cube. The left side and right side faces are coloured blue. The third image shows a cabinet projection of a cube. The front and back faces are coloured pink. The fourth image shows an isometric projection of a cube. The top face is coloured orange, the left face is coloured pink, and the right face is coloured blue. The fifth image shows the net of a cube. There are four joined squares in a horizontal line. Two additional squares have been joined above and below the second square in the line. The first and third square in the line are coloured blue and the second and forth squares are coloured pink. The additional squares are coloured orange.
A net of a 3D shape (a cube).

  • The is the total area of all the of the shape. For example, the surface area of a cube is the total area of all six square faces. This is 6 × side².

  • Surface area is measured in square units including cm² and m².

  • The of the square is the edge of the cube and is the length, width and height dimensions of the 3D shape.

  • A has six faces and opposite pairs of faces are . The of a cuboid are paired to give three congruent pairs of faces. For example, a cuboid with dimensions 2 cm × 3 cm × 4 cm has two faces which measure 2 cm × 3 cm, two which measure 2 cm × 4 cm and two which measure 3 cm × 4 cm.

  • The of a 3D shape is what a shape looks like when it is opened out into a 2D shape. The net can help to show the areas of each face that make up the surface area of a shape.

A series of five images. Each image shows the same cube. The first image shows a cabinet projection of a cube. The top and base faces are coloured orange. The second image shows a cabinet projection of a cube. The left side and right side faces are coloured blue. The third image shows a cabinet projection of a cube. The front and back faces are coloured pink. The fourth image shows an isometric projection of a cube. The top face is coloured orange, the left face is coloured pink, and the right face is coloured blue. The fifth image shows the net of a cube. There are four joined squares in a horizontal line. Two additional squares have been joined above and below the second square in the line. The first and third square in the line are coloured blue and the second and forth squares are coloured pink. The additional squares are coloured orange.
A net of a 3D shape (a cube).
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Calculating the surface area of a cube

A cube has six congruent square faces. The total area of the faces is the surface area of the cube.

To work out the surface area of a cube:

  1. one edge of the cube. This gives the area of one square face.
  2. Multiply the area of one square face by six.

To find the length of an edge of a cube:

  1. Divide the total surface area by six. This gives the area of one square face.
  2. Find the .

Examples

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  1. A series of three images. Each image shows the same cube. The first image shows a cabinet projection of a cube. The top and base faces are coloured orange. The second image shows a cabinet projection of a cube. The left side and right side faces are coloured blue. The third image shows a cabinet projection of a cube. The front and back faces are coloured pink.

    A cube has six faces. Each face of a cube is a square.

Question

What is the total surface area of a cube with an edge of 11 mm?

The image shows an isometric projection of a cube. The length of the cube has been labelled as eleven millimetres. The cube is coloured grey.

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Calculating the surface area of a cuboid

A cuboid has three pairs of faces:

  • The top face and the base face.
  • The left and right faces.
  • The front and back faces.

To work out the total surface area of a cuboid:

  1. Find the area of the top and base faces. This is length × width × 2
  2. Find the area of the right and left faces. This is width × height × 2
  3. Find the area of the front and back faces. This is length × height × 2
  4. Add the face areas to find the total surface area.

The formula for the surface area of a cuboid with the dimensions 𝒍 × 𝒘 × 𝒉 can be given as:

Surface area = 2𝒍𝒘 + 2𝒘𝒉 + 2𝒍𝒉 or surface area = 2(𝒍𝒘 + 𝒘𝒉 + 𝒍𝒉).

Examples

Skip image gallery
  1. A series of three images. Each image shows the same cuboid. The first image shows a cabinet projection of a cuboid. The top and base faces are coloured orange. The second image shows a cabinet projection of a cuboid. The left side and right side faces are coloured blue. The third image shows a cabinet projection of a cuboid. The front and back faces are coloured pink.

    A cuboid has three pairs of congruent faces. The top and base faces are congruent. The left and right faces are congruent. The front and back faces are congruent.

Question

Find the total surface area of the cuboid.

The image shows a cabinet projection of a cuboid. The length is labelled as twelve centimetres, the width is labelled as three centimetres, and the height is labelled as seven centimetres.

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Practise finding the surface area

Practise finding the surface area of cubes and cuboids with this quiz. You may need a pen and paper to help you with your answers.

Quiz

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