Find the volume of any prism — cuboid, triangular, trapezium or L-shaped — by multiplying the cross-section area by the length. It is on Foundation and Higher, aimed at grade 4. Free questions with answers are on this page. Worked examples show each line before you try the questions.
A prism has the same cross-section all the way along. Volume =area of cross-section×length. A triangular prism uses 21bh for the triangle, then times the length. A cuboid is the special case lwh. Units are cm³.
Compound prisms add or subtract volumes. A missing triangular tunnel through a cuboid is cuboid minus prism. Convert mm and cm before you multiply, and convert cm³ to litres with 1000 cm³ =1 litre if the answer wants litres.
Volume of any prism = area of cross-section × length. A cuboid is lwh. A triangular prism needs 21bh first. Units are cm³; an 'how many small cubes fill the box' is volume ÷ volume.
Objectives
A prism has the same cross-section all the way along.
Volume = area of cross-section × length.
The cross-section is a rectangle, so area = length × width, and volume = that × height.
Key points
Recognise a prism: the same cross-section all the way along.
Find the area of the cross-section (rectangle, triangle, trapezium or compound shape).
Multiply the cross-section area by the length.
Convert between cm³, litres and m³ when the context needs it.
Worked examples
Example 1
A prism has a cross-section of area 24 cm² and a length of 9 cm. What is the volume in cm³?
2 marks
Volume of a prism = area of cross-section × length.
Volume = 24 × 9.
24 × 9 = 216 cm³.
Answer: 216
Common slips
Slip: Skip this step: Volume of a prism = area of cross-section × length. Every step in the working is needed. Skipping one loses the method.
Slip: Volume = 27 × 9. That changes a number in the working, so the step no longer follows from the one before.
Slip: 28 × 9 = 216 cm³. That does not match the working above it.
Example 2
A cuboid measures 7 cm by 3 cm by 5 cm. Work out its volume in cm³.
2 marks
The cross-section is 7 × 3 = 21 cm².
Volume = 21 × 5.
21 × 5 = 105 cm³.
Answer: 105
Common slips
Slip: The cross-section is 9 × 3 = 21 cm². That changes a number from the question, so it answers a different question.
Slip: Volume = 24 × 5. That changes a number in the working, so the step no longer follows from the one before.
Slip: 25 × 5 = 105 cm³. That does not match the working above it.
Example 3
A triangular prism has a triangular end with base 8 cm and perpendicular height 3 cm. The prism is 3 cm long. Work out its volume in cm³.
3 marks
Area of the end = ½ × 8 × 3 = 12 cm².
Volume = area × length = 12 × 3.
12 × 3 = 36 cm³.
Answer: 36
Common slips
Slip: Area of the end = ½ × 10 × 3 = 12 cm². That changes a number from the question, so it answers a different question.
Slip: Volume = area × length = 15 × 3. That changes a number in the working, so the step no longer follows from the one before.
Slip: 16 × 3 = 36 cm³. That does not match the working above it.
Questions and answers
GCSE Maths volume of a prism questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
A tank is a cuboid 20 cm by 50 cm by 30 cm. How many litres of water does it hold when it is full?
Show answer
Answer: 30
Volume = 20 × 50 × 30 = 30000 cm³.
1 litre = 1000 cm³.
M1 — Volume = 20 × 50 × 30 = 30000 cm³.
A1 — Answer 30
Question 2 Easy2 marks
A prism has a volume of 24 cm³. Its cross-section has an area of 6 cm². How long is the prism?
Show answer
Answer: 4
Volume = area × length, so length = volume ÷ area.
Length = 24 ÷ 6.
M1 — Volume = area × length, so length = volume ÷ area.
A1 — Answer 4
Question 3 Medium2 marks
A triangular prism has a triangular end with base 8 cm and perpendicular height 8 cm. The prism is 4 cm long. Work out its volume in cm³.
Show answer
Answer: 128
Area of the end = ½ × 8 × 8 = 32 cm².
Volume = area × length = 32 × 4.
M1 — Area of the end = ½ × 8 × 8 = 32 cm².
A1 — Answer 128
Question 4 Medium2 marks
A tank is a cuboid 10 cm by 20 cm by 50 cm. How many litres of water does it hold when it is full?
Show answer
Answer: 10
Volume = 10 × 20 × 50 = 10000 cm³.
1 litre = 1000 cm³.
M1 — Volume = 10 × 20 × 50 = 10000 cm³.
A1 — Answer 10
Question 5 Hard2 marks
A cuboid measures 6 cm by 10 cm by 8 cm. Work out its volume in cm³.
Show answer
Answer: 480
The cross-section is 6 × 10 = 60 cm².
Volume = 60 × 8.
M1 — The cross-section is 6 × 10 = 60 cm².
A1 — Answer 480
Question 6 Hard2 marks
A triangular prism has a triangular end with base 10 cm and perpendicular height 8 cm. The prism is 8 cm long. Work out its volume in cm³.
Show answer
Answer: 320
Area of the end = ½ × 10 × 8 = 40 cm².
Volume = area × length = 40 × 8.
M1 — Area of the end = ½ × 10 × 8 = 40 cm².
A1 — Answer 320
Question 7 Exam-style3 marks
A triangular prism has a triangular end with base 6 cm and perpendicular height 7 cm. The prism is 9 cm long. Work out its volume in cm³.
Show answer
Answer: 189
Area of the end = ½ × 6 × 7 = 21 cm².
Volume = area × length = 21 × 9.
21 × 9 = 189 cm³.
M1 — Area of the end = ½ × 6 × 7 = 21 cm².
M1 — Volume = area × length = 21 × 9.
A1 — Answer 189
Common mistakes
Most lost marks on this topic are one slip.
Adding the area to the length.
Multiply them.
Using a sloping side as the height of the triangular end.
The height of the triangle is perpendicular to its base.
Giving the answer in cm².
Volume is in cm³.
Spot the slip
Volume is measured in
cubic units
square units
centimetres
Show the slip
cubic units Volume fills space, so the unit is cubed.
Exam tips
This topic can appear on a calculator or a non-calculator paper. Show enough working for a method mark.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Write 'area of cross-section = …' as a separate line; it is a method mark on its own.
For an L-shape or T-shape cross-section, draw a line to split it into rectangles and label each one.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.