5.4

Volume

Cambridge IGCSE Mathematics (0580)  · Unit 5: Mensuration  · 9 flashcards

Volume is topic 5.4 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 5 — Mensuration , alongside Perimeter and area, Circles - circumference and area and Surface area.  In one line: Volume is the amount of space occupied by a three-dimensional object. Common units include cubic centimetres (cm³) and cubic metres (m³). Note that 1 litre = 1000 cm³.

This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.

The deck below contains 9 flashcards — 2 definitions and 5 key concepts — covering the precise wording mark schemes reward.  Use the 2 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.

Key definition

Volume. What units are commonly used for volume

Volume is the amount of space occupied by a three-dimensional object. Common units include cubic centimetres (cm³) and cubic metres (m³). Note that 1 litre = 1000 cm³.

Questions this Volume deck will help you answer

Definition Flip

Define volume. What units are commonly used for volume?

Answer Flip

Volume is the amount of space occupied by a three-dimensional object. Common units include cubic centimetres (cm³) and cubic metres (m³). Note that 1 litre = 1000 cm³.

Key Concept Flip

State the formula for the volume of a cuboid.

Answer Flip

Volume of a cuboid = length × width × height, or V = lwh.

Example: a cuboid with length 5cm, width 3cm, and height 2cm has a volume of 30cm³.
Key Concept Flip

State the formula for the volume of a cylinder.

Answer Flip

Volume of a cylinder = πr²h, where r is the radius of the circular base and h is the height. A cylinder with radius 4cm and height 10cm has a volume of π(4²)(10) ≈ 502.65 cm³.

Key Concept Flip

State the formula for the volume of a sphere.

Answer Flip

Volume of a sphere = (4/3)πr³, where r is the radius of the sphere. A sphere with radius 3cm has a volume of (4/3)π(3³) ≈ 113.10 cm³.

Key Concept Flip

State the formula for the volume of a right pyramid with a square base.

Answer Flip

Volume of a pyramid = (1/3) × base area × height = (1/3)l²h, where l is the side length of the square base and h is the perpendicular height. For

Example: A pyramid with a 4cm x 4cm base and height 6cm has a volume of 32cm³.
Key Concept Flip

State the formula for the volume of a cone.

Answer Flip

Volume of a cone = (1/3)πr²h, where r is the radius of the circular base and h is the perpendicular height. A cone with radius 2cm and height 5cm has a volume of (1/3)π(2²)(5) ≈ 20.94 cm³.

Key Concept Flip

A rectangular tank is 2m long, 1.5m wide, and 1m high. How many litres of water can it hold when full?

Answer Flip

Volume = lwh = 2m × 1.5m × 1m = 3m³. Since 1 m³ = 1000 litres, the tank can hold 3 × 1000 = 3000 litres.

Key Concept Flip

A cylinder has a volume of 500 cm³ and a height of 10 cm. What is the radius of its base?

Answer Flip

Using the formula V = πr²h, we have 500 = πr²(10). Solving for r, we get r² = 500/(10π) ≈ 15.92. Therefore, r ≈ √15.92 ≈ 3.99 cm.

Definition Flip

Define Capacity. How is it related to volume?

Answer Flip

Capacity is the amount a container can hold, typically measured in litres (L) or millilitres (mL). Volume is the space an object occupies. The capacity of a container is equivalent to its internal volume.

Example: a rectangular fish tank with internal dimensions 50cm x 30cm x 40cm has a volume of 60,000 cm³, which is equivalent to a capacity of 60 L.

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Read revision notes with definitions, equations, and exam tips.

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Test yourself

Practice with MCQ questions to check your understanding.

Take Mathematics Quiz
5.3 Surface area 6.1 Trigonometric ratios

Key Questions: Volume

Define volume. What units are commonly used for volume?

Volume is the amount of space occupied by a three-dimensional object. Common units include cubic centimetres (cm³) and cubic metres (m³). Note that 1 litre = 1000 cm³.

Define Capacity. How is it related to volume?

Capacity is the amount a container can hold, typically measured in litres (L) or millilitres (mL). Volume is the space an object occupies. The capacity of a container is equivalent to its internal volume.

Example: a rectangular fish tank with internal dimensions 50cm x 30cm x 40cm has a volume of 60,000 cm³, which is equivalent to a capacity of 60 L.

Tips to avoid common mistakes in Volume

More topics in Unit 5 — Mensuration

Volume sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.

5.1 Perimeter and area

10 flashcards
5.2 Circles - circumference and area

9 flashcards
5.3 Surface area

10 flashcards

Cambridge syllabus keywords to use in your answers

These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.

volume capacity cube cuboid prism cylinder cone sphere pyramid cubic units cm3 m3 litres

Key terms covered in this Volume deck

Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.

Volume. What units are commonly used for volume
Capacity. How is it related to volume

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Cambridge maths notation guide

Notation conventions Cambridge expects in your answers

How to study this Volume deck

Start in Study Mode, attempt each card before flipping, then rate Hard, Okay or Easy. Cards you rate Hard come back within a day; cards you rate Easy push out to weeks. Your progress is saved in your browser, so come back daily for 5–10 minute reviews until every card reads Mastered.