A cuboid has some rectangular faces. We can be expected to find the volume of a cuboid by counting the cubes.
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| For example: Calculate the volume of the cuboid, drawn below. |
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It is best to work in layers as not all of the cubes can be seen. We can see 12 cubes in the top layer. There are 3 layers, so the total number of cubes is 3 x 12 = 36 cubes. Volume of the cuboid = 36 cubes. |
Formula for the volume of a cuboid
This can be used when the dimensions of the cuboid are given. |
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Volume of a cuboid
= Length x Width x Height |
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| For example: Calculate the volume of the cuboid shown below. |
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Volume = 10 x 6 x 5 = 300 cm3 (Note the cubic units for volume)
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Note: As with area, volumes can be added or subtracted.
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| For example: A cuboid has had a rectangular section removed from the centre, as shown in the diagram below. Calculate the volume of the remainder. |
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Total volume = 20 x 10 x 6 = 1 200 cm3
Volume of section cut out = 5 x 10 x 2 = 100 cm3
Volume of remainder = 1 200 – 100 = 1 100 cm3
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Prism
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Volume of a prism
A prism is a 3D object whose cross section is constant, along its length. An example is drawn below.
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| Formula for the volume of a prism |
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| Volume of a prism = Area of cross section x Length |
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| For example: |
Volume of the triangular prism (above) = Area of triangle x length
= (½ x 10 x 6) x 20
= 30 x 20
Volume = 600 cm3 |
