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8.5 Volume of Prisms

GCSE Maths Foundation · Edexcel · Chapter 8: Perimeter, Area, and Volume 1

A free GCSE Maths Foundation lesson for Edexcel (9–1) from OBA School: volume of cubes, cuboids and other prisms, and working backwards from a volume. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with interactive activities, practice quizzes and printable worksheets, in our free online course.

What you will learn

  • Find the volume of a shape by counting cubes and using V = l × w × h
  • Find the volume of any prism using area of cross-section × length
  • Work backwards from a volume to find a missing length or area
  • Solve problems such as how many small boxes fit into a larger box

Key words

  • Volume: The amount of space inside a 3D solid. Units: cm³, m³, …
  • Cubic centimetre: 1 cm³ is the volume of a cube with edges 1 cm long.
  • Cross-section: The 2D shape you see if you slice straight through a prism. It is the same all the way along.
  • Prism: A solid with a constant cross-section, such as a cuboid, triangular prism or cylinder.

Volume of a cuboid

Volume counts how many unit cubes fit inside. A cuboid 5 cm by 3 cm by 2 cm has 5 × 3 = 15 cubes in each layer and 2 layers.

Key fact: Volume of a cuboid = length × width × height. Volume of a cube = side × side × side = side³

Worked example: cuboid and cube

Cuboid: 5 × 3 × 2 = 30 cm³.
Cube with edges 4 cm: 4 × 4 × 4 = 64 cm³.

Answer: 30 cm³ and 64 cm³

Volume of a prism

Every prism is a stack of identical slices. Find the area of the cross-section, then multiply by the length.

Key fact: Volume of a prism = area of cross-section × length

Worked example: a triangular prism

Cross-section: 1/2 × 4 × 3 = 6 cm².
Volume = 6 × 10 = 60

Answer: 60 cm³

Worked example: given the cross-section area

An L-shaped prism has cross-section area 22 cm² and length 8 cm.
Volume = 22 × 8 = 176

Answer: 176 cm³

Working backwards

Write the formula, put in what you know, then use inverse operations.

Worked example: missing height

A cuboid has volume 120 cm³, length 6 cm and width 4 cm. Find its height.
6 × 4 × h = 120, so 24h = 120 and h = 120 ÷ 24 = 5.

Answer: 5 cm

Worked example: missing cross-section

A prism has volume 180 cm³ and length 12 cm. Find the area of its cross-section.
Area × 12 = 180, so area = 180 ÷ 12 = 15.

Answer: 15 cm²

Packing problems

To find how many small boxes fit in a big box, see how many fit along each edge, then multiply. Dividing the volumes only works when the boxes fit exactly.

Worked example: cubes in a box

How many 2 cm cubes fit in a box 10 cm by 6 cm by 4 cm?
Along each edge: 10 ÷ 2 = 5, 6 ÷ 2 = 3, 4 ÷ 2 = 2. 5 × 3 × 2 = 30

Answer: 30 cubes

Exam tip: Volume answers are in cubic units: cm³, m³. Area answers are in square units.

Common mistakes

  • Multiplying the lengths of three sides of a triangular prism instead of using the cross-section area.
  • Forgetting to halve when the cross-section is a triangle.
  • Writing the units as cm² instead of cm³.
  • Dividing volumes in packing problems when the boxes do not fit exactly along each edge.

Revision questions

Try these, then check your answers below each one.

Question 1. Work out the volume of a cuboid 7 cm by 4 cm by 3 cm.

Answer: 84 cm³

Working: 7 × 4 × 3 = 84 cm³.

Question 2. Work out the volume of a cube with edges 5 cm long.

Answer: 125 cm³

Working: 5³ = 125 cm³.

Question 3. A prism has a cross-section of area 18 cm² and a length of 11 cm. Work out its volume.

Answer: 198 cm³

Working: 18 × 11 = 198 cm³.

Related lessons

Continue in the full course

This lesson is section 8.5 (EGCMF0805) of our free GCSE Maths Foundation course. In the full course you get every video for this section, an animated interactive lesson, a self-marking practice quiz, a printable worksheet with a mark scheme, and your progress saved. Go to the full GCSE Maths Foundation course.

 

 

 

 

 

 

 

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