GCSE Maths / Edexcel

Volume of cuboids and prisms

Find volumes of cuboids and prisms by identifying the repeated cross-section, calculating its area, and multiplying by the length.

Geometry and MeasuresFoundation and HigherGrades 3 to 6Skill

Curriculum path: GCSE Maths > Edexcel > Geometry and Measures > Volume of cuboids and prisms

Pearson Edexcel GCSE Maths geometry G16: know and apply formulae to calculate volume of cuboids and prisms.

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Revision notes

Theory, examples, and quick checks.

Keep the method short, then practise straight away. This note is written for GCSE Maths Edexcel students who need clear working and reliable method marks.

Theory

Volume is the amount of space inside a 3D shape. Volume uses cubic units such as cm³ or m³.

For a cuboid, volume = length x width x height.

A prism has the same cross-section all the way through.

For any prism, volume = area of cross-section x length.

The cross-section might be a rectangle, triangle or trapezium. Find that area first, then multiply by the prism length.

Check that all lengths are in the same unit before calculating volume.

For a triangular prism, find the triangle area using 1/2 x base x height, then multiply by the prism length.

If the volume and cross-section area are known, find the prism length by dividing volume by cross-section area.

Do not confuse volume with surface area. Volume fills the inside; surface area covers the outside.

Key ruleVolume of a prism = area of cross-section x length.

Diagram guide

Prism volume structureA prism repeats the same cross-section through its length. Find the cross-section area first.

Triangular prismThe repeated cross-section is a triangle, so calculate triangle area before multiplying by length.

Missing prism lengthRearrange the prism formula: length = volume divided by cross-section area.

Worked examples

Cuboid

Find the volume of a cuboid 8 cm by 5 cm by 4 cm.

Example: cuboid volumeA cuboid is a rectangular prism, so multiply the three dimensions.

Volume = length x width x height.
8 x 5 x 4 = 160.

Answer: 160 cm³

Triangular prism

A triangular prism has cross-section area 24 cm² and length 10 cm. Find its volume.

Example: triangular prismThe triangle area has already been given, so multiply it by the prism length.

Volume = cross-section area x length.
24 x 10 = 240.

Answer: 240 cm³

Find missing length

A prism has volume 300 cm³ and cross-section area 25 cm². Find its length.

Example: missing lengthDivide the volume by the cross-section area.

Volume = cross-section area x length.
Length = 300 / 25.

Answer: 12 cm

Find the cross-section first

A triangular prism has triangular cross-section base 8 cm and height 5 cm. The prism length is 12 cm. Find the volume.

Example: cross-section firstThis is a two-stage question: triangle area, then prism volume.

Triangle area = 1/2 x 8 x 5 = 20 cm².
Volume = 20 x 12.
20 x 12 = 240.

Answer: 240 cm³

Common mistakes

Writing square units instead of cubic units.
Adding the three dimensions instead of multiplying.
Using perimeter of the cross-section instead of area.
Forgetting to find the triangular cross-section area before multiplying.
Finding surface area when the question asks for volume.
Dividing by the prism length when the question gives cross-section area and asks for volume.

Quick exercise

Try these before moving to the exam-style questions.

Find the volume of a cuboid 6 cm by 4 cm by 3 cm.
Quick check: cuboidMultiply length, width and height.
A prism has cross-section area 15 cm² and length 9 cm. Find its volume.
Quick check: prism formulaVolume = cross-section area x length.
A cuboid has volume 120 cm³, length 10 cm and width 4 cm. Find its height.
Quick check: missing heightDivide volume by the two known dimensions.
A triangular prism has cross-section area 18 cm² and length 7 cm. Find its volume.
Quick check: triangular prismThe cross-section area is already given.
Find the volume of a cube with side length 5 cm.
Quick check: cubeA cube is a cuboid with all sides equal.

Exam-style questions

Practise the same skill at three levels.

These are original GCSE-style questions with mark schemes, common wrong answers, and AI marking guidance so feedback stays close to exam expectations.

Basic GCSE styleFoundationNon-calculator2 marks

A cuboid measures 7 cm by 4 cm by 3 cm. Work out its volume.

Question diagram: cuboid volumeMultiply the three dimensions to fill the cuboid.

Your answer and working

volumecuboidfoundation geometry

Standard exam styleFoundation and HigherCalculator3 marks

A prism has cross-section area 32 cm² and length 11 cm. Work out the volume of the prism.

Question diagram: prism volumeThe repeated cross-section area is given.

Your answer and working

prism volumecross-sectionmethod marks

ChallengeFoundation and HigherCalculator5 marks

A triangular prism has triangular cross-section with base 8 cm and height 5 cm. The prism length is 12 cm. Work out the volume.

Question diagram: triangular prismFind the triangular cross-section area first.

Your answer and working

triangular prismvolumecross-section area

Next step in the app

Use the notes with a real answer.

Reading the method helps, but the progress comes from answering, marking, and fixing one question at a time.

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