Functional Skills: Volume

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Functional Skills: Volume Revision

Volume of 3D Shapes

The volume of an object is how much space it takes up. Volume involves lengths being multiplied 3 times – so the units for length need to be multiplied together 3 times too. Therefore, we get units like metres cubed (m^3), centimetres cubed (cm^3) and millimetres cubed (mm^3) for volume.

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Volume of Cubes and Cuboids

The volume of a cuboid is given by:

\text{Volume of cuboid} = \textcolor{blue}{\text{length} \times \text{width} \times \text{height} = l \times w \times h}

 

For a cube, all sides are the same length, so the volume of a cube is given by:

\text{Volume of cube} = \textcolor{blue}{\text{length} \times \text{length} \times \text{length} = l \times l \times l = l^3}

 

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Volume of Prisms and Cylinders

The volume of a prism is given by:

\text{Volume of prism} = \textcolor{red}{\text{cross-sectional area}} \times \textcolor{limegreen}{\text{length}}

This is the case for any prism, including cubes and cuboids. The cross-sectional area on a prism is the area of the front or back face. For a triangular prism, the cross-sectional area is a triangle and for a cylinder (which is like a prism) it is a circle.

So, the volume of a cylinder is given by

\text{Volume of cylinder} = \textcolor{red}{\pi r^2} \times \textcolor{limegreen}{\text{length}}

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Example 1: Volume of a Cuboid

Below is a rectangle. The rectangle has a length of 18 cm, a width of 8 cm and a height of 5 cm.

Calculate the volume of the cuboid.

[2 marks]

We need to multiply the length by the width by the height.

\text{Volume} = \text{length} \times \text{width} \times \text{height} = 18 \times 8 \times 5 = 720 cm^3

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Example 2: Volume of a Prism

Below is a triangular prism. The triangular face has base of 6\text{ cm} and height of 5\text{ cm}. The length of the prism is 3.5\text{ cm}.

Calculate the volume of this prism.

[3 marks]

The first step in this question is to work out the area of the cross-section, so the triangle.

We can do this as follows,

\dfrac{1}{2}(6\times5)=15\text{ cm}^2

The next step is to multiply the cross-sectional area by the length of the prism,

 \text{Volume} = 15\times3.5=52.5\text{ cm}^3

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Functional Skills: Volume Example Questions

Multiply the length by the height by the width:

 

Volume = 3\times12 \times16=576 cm^3

The volume of a cube is calculated by cubing the length of one of its sides:

 

Volume = 5 \times 5 \times 5 = 125 cm^3

Radius = 8 \div 2 = 4 cm

Area of circle = \pi r^2 = 3.14 \times 4^2 = 50.24 cm^2

Volume = 50.24 \times 5 = 251.2 = 251 cm^3 (nearest whole number)

Additional Resources

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Exam Tips Cheat Sheet

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Formula Booklet

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Functional Skills: Volume Worksheet and Example Questions

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