Volume of cubes and cuboids

Part of MathsPerimeter, Area, Volume

Key points

A series of four images. Each image shows a different size cube made up of individual cubes. Each cube is drawn in an isometric perspective. The first image is a one by one by one cube. Written above: one cubed. Written below: one multiplied by one multiplied by one equals one. The second image is a two by two by two cube. Written above: two cubed. Written below: two multiplied by two multiplied by two equals eight. The third image is a three by three by three cube. Written above: three cubed. Written below: three multiplied by three multiplied by three equals twenty seven. The fourth image is a four by four by four cube. Written above: four cubed. Written below: four multiplied by four multiplied by four equals sixty four. In each cube the faces pointing upwards are coloured orange, the faces pointing towards the left are coloured pink, and the faces pointing towards the right are coloured blue.
To calculate the volume of a cube, the length, width and height dimensions are multiplied.

  • and are measured in cubic units, including cm³ and m³.

  • To calculate volume and capacity, three dimensions are used: length, width and height.

  • When a or is drawn using individual cubes, the volume can be found by counting the . This method can also be used for compound 3D shapes made up of two or more cuboids.

A series of four images. Each image shows a different size cube made up of individual cubes. Each cube is drawn in an isometric perspective. The first image is a one by one by one cube. Written above: one cubed. Written below: one multiplied by one multiplied by one equals one. The second image is a two by two by two cube. Written above: two cubed. Written below: two multiplied by two multiplied by two equals eight. The third image is a three by three by three cube. Written above: three cubed. Written below: three multiplied by three multiplied by three equals twenty seven. The fourth image is a four by four by four cube. Written above: four cubed. Written below: four multiplied by four multiplied by four equals sixty four. In each cube the faces pointing upwards are coloured orange, the faces pointing towards the left are coloured pink, and the faces pointing towards the right are coloured blue.
To calculate the volume of a cube, the length, width and height dimensions are multiplied.
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Finding volume by counting cubes and using cube numbers

  • Volume is measured in cubic units. These are unit cubes which may be mm³, cm³ and m³.

  • There are multiple ways of finding the volume of a cube. For example, counting the cubes of the top layer and by cubing one of the cube’s sides.

  • To find the volume by counting cubes:

  1. Count the unit cubes that make the top layer of the cube.

  2. Multiply the number of cubes in the top layer by the total number of layers it has.

  • To calculate the volume of a cube:

    • Cube the length of one edge of the cube. For an edge of length \(x\), the volume of a cube is given by the formula \(V\) = \(x\)³.

  • To calculate the edge of a cube:

    • the volume. Cube root is the of cube.

Examples

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  1. A series of two images. Each image shows a different size cube made up of individual cubes. Each cube is drawn in an isometric projection. The first image is a one by one by one cube. Written above: unit cube equals one centimetre cubed. The second image is a four by four by four cube. In each cube the faces pointing upwards are coloured orange, the faces pointing towards the left are coloured pink, and the faces pointing towards the right are coloured blue.

    Volume is measured in cubic units. Each unit cube represents 1 cm³. Find the volume of the cube.

Question

Each unit cube is 1 cm³. Find the volume of the cube.

A series of two images. Each image shows a different size cube made up of individual cubes. Each cube is drawn in an isometric projection. The first image is a one by one by one cube. Written above: unit cube equals one centimetre cubed. The second image is a three by three by three cube. The cubes are coloured grey.

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Calculating the volume of a cuboid

  • To find the volume of a cuboid by counting:

  1. Count the unit cubes that make the top layer of the cuboid.

  2. Multiply the number of cubes in the top layer by the number of layers.

  • To calculate the volume of a cuboid:

    • Multiply the length by width by height. \(V\) = \(lwh\). This can be done in any order, the answer will be the same.

Examples

Skip image gallery
  1. A series of two images. The first image is a one by one by one cube. It is drawn in an isometric perspective. Written above: unit cube equals one centimetre cubed. The second image is a cuboid of length, three cubes, width, two cubes, and height, five cubes. It is drawn in an isometric perspective showing each of the individual cubes. In each shape the faces pointing upwards are coloured orange, the faces pointing towards the left are coloured pink, and the faces pointing towards the right are coloured blue.

    Each unit cube represents 1 cm³. Find the volume of the cuboid.

Question

What is the volume of the cuboid?

The image shows a cabinet projection of a cuboid. The length is labelled as nine millimetres, the width is labelled as four millimetres, and the height is labelled as five millimetres. Written top left: volume equals length multiplied by width multiplied by height; example two.

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Practise finding the volume of cubes and cuboids

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

Quiz

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Real-life maths

Pictures of boxes of various sizes on a conveyer belt.
The cost of a delivery charge depends on the volume of a package.

  • A delivery service should ensure that the boxes used have the capacity to hold the articles that have been purchased. The cost of sending a package can be related to its volume. This may be referred to as volumetric weight.

  • Volumetric weight is used in the courier and logistics industry to calculate how much space an item is going to take up. If your item is light in weight but large in size, and therefore takes up a lot of room, the cost charged will reflect this.

Pictures of boxes of various sizes on a conveyer belt.
The cost of a delivery charge depends on the volume of a package.
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Game - Divided Islands

Use your maths skills to help the islanders of Ichi build bridges and bring light back to the islands in this free game from BBC Bitesize.

Divided Islands
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