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Volume of a Prism

FoundationHigherAQAEdexcelOCR

This free Foundation and Higher GCSE Maths worksheet on volume of a prism helps you revise calculating the volume of prisms. Questions build from straightforward to exam standard, with full worked answers in the mark scheme — ideal for revision or homework. Suitable for AQA, Edexcel and OCR. Volume of a prism = cross-sectional area × length.

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These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.

Foundation

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Higher

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Topic overview

The volume of a prism is the area of its cross-section multiplied by its length. This single rule covers every prism, whatever the shape of the end.

So a cuboid's volume is length times width times height, because the cross-section is a rectangle. A triangular prism uses the triangle's area times the length.

Volume is measured in cubed units, because three dimensions are multiplied together. Getting the units right is worth a mark and also serves as a check that you have done the right calculation.

Revision notes

The general formula

Volume equals the area of the cross-section multiplied by the length.

For a triangular prism with cross-section area \(12\)cm² and length \(9\)cm: \(12 \times 9 = 108\)cm³.

Identifying the cross-section

The cross-section is the shape that stays the same all the way through, and the length is measured perpendicular to it.

A prism lying on its side can be confusing, so identify the two identical ends rather than assuming the longest dimension is the length.

Cuboids and cylinders

A cuboid's cross-section is a rectangle, so its volume is \(lwh\).

A cylinder's cross-section is a circle, so its volume is \(\pi r^2 h\). Both are just the general rule applied to a particular shape.

Key points

  • Volume of a prism is cross-section area times length.
  • The cross-section is the shape that stays constant.
  • Cuboid volume is \(l \times w \times h\).
  • Cylinder volume is \(\pi r^2 h\).
  • Volume is measured in cubed units.
  • The length is perpendicular to the cross-section.

Worked examples

Example 1

Find the volume of a prism with cross-section area \(20\)cm² and length \(7\)cm.

Working

\[20 \times 7\]multiply cross-section area by length
\[= 140\text{cm}^3\]state the volume in cubed units

Example 2

Find the volume of a cuboid \(8 \times 5 \times 3\)cm.

Working

\[8 \times 5 = 40\text{cm}^2\]find the cross-section area
\[40 \times 3\]multiply by the remaining dimension
\[= 120\text{cm}^3\]state the volume

Example 3

Find the volume of a triangular prism with base \(6\)cm, height \(4\)cm and length \(10\)cm.

Working

\[\frac{1}{2} \times 6 \times 4 = 12\text{cm}^2\]find the triangle's area
\[12 \times 10\]multiply by the prism's length
\[= 120\text{cm}^3\]state the volume

Common mistakes

  • Using squared units.

    Volume needs cm³, since three dimensions are multiplied.

  • Choosing the wrong face as the cross-section.

    It is the shape that stays the same throughout, not necessarily the one facing you.

  • Forgetting to halve for a triangular cross-section.

    The triangle's area still needs the ½.

  • Mixing units.

    Convert everything to one unit before multiplying.

Exam tips

  • Identify the cross-section before calculating anything.
  • Work out the cross-section area as a separate step.
  • Always use cubed units for volume.
  • Check the length is perpendicular to the cross-section.

Key terms

Prism
A solid with a constant cross-section.
Cross-section
The shape that remains the same throughout the solid.
Volume
The space inside a 3D shape.
Cubed units
Units such as cm³ used for volume.

Related topics

Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.