Volume of a Cuboid: l × w × h

ME13Volume of Cuboids

Layers of centimetre cubes.

Volume of a cuboid = length × width × height — layers of unit cubes.

How many 1 cm cubes fill the box?

5 × 3 × 4 = 60 cm³

One layer = 5 × 3 = 15 cubes; 4 layers = 60 cubes.

Learn the 3-Step Method

1Find one layer.

The bottom layer holds length × width cubes: 5 × 3 = 15.

5 × 3 = 15

2Count the layers.

The height says how many layers stack up: 4.

4 layers

3Multiply.

15 × 4 = 60 cubes → 60 cm³.

15 × 4 = 60

💡 Key IdeaVolume is measured in cubic units — cm³, m³ — because we're counting cubes, not squares.

Worked Example

A toy box is 40 cm long, 30 cm wide and 20 cm tall. Find its volume.

Layer

40 × 30 = 1200

→

Stack

1200 × 20 = 24000

→

✓ Answer

24 000 cm³

Watch Out! Common Mistakes

Only multiplying two sides.

V = 5 × 3 = 15 cm³ ✕

Wrong! That’s one layer (area). Multiply by the height too: 5 × 3 × 4 = 60 cm³.

Wrong unit.

V = 60 cm² ✕

Wrong! Volume counts cubes: cm³. (cm² is area — flat squares.)

Order worries.

3 × 5 × 4 vs 5 × 4 × 3

Relax! Multiplication order doesn’t matter — all orders give 60. Pick the easiest pairing.

⬇ Cheat Sheet

VOLUME OF CUBOIDS

Volume = length × width × height.
Think: one layer, times the number of layers.
Answer in cubic units: cm³, m³.
Any multiplication order works.

Examples: 5×3×4 = 60 cm³ · 40×30×20 = 24 000 cm³

📖 Continue Your Journey

✓ ME1 Units of Length ✓ ME2 Converting Length ✓ ME3 Units of Mass ✓ ME4 Converting Mass ✓ ME5 Units of Capacity ✓ ME6 Converting Capacity ✓ ME7 Reading Scales ✓ ME8 Perimeter ✓ ME9 Area of Rectangles ✓ ME10 Area of Triangles ✓ ME11 Area of Parallelograms ✓ ME12 Compound Shapes ME13 Volume of Cuboids ME14 Telling the Time ME15 Time Calculations ME16 Money Calculations ME17 Imperial and Metric Units ME18 Measurement Problem Solving

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Next Lesson: ME14 Telling the TimeAnalogue, digital and the 24-hour clock.

📄 Free printable: Download the Volume of Cuboids cheat sheet (PDF) — keep it by your child's desk.

Quick summary

Volume of a cuboid = length × width × height.
Think in layers: one layer of cubes, times the number of layers.
Volume uses cubic units: cm³, m³.
Multiplication order doesn't matter — choose easy pairings.

Frequently asked questions

What is the formula for the volume of a cuboid?

Length × width × height. A 5 × 3 × 4 cm box holds 60 cm³.

Why is volume measured in cm³?

Because it counts how many 1 cm × 1 cm × 1 cm cubes fit inside — cubes, not flat squares.

When do children learn volume?

Counting cubes starts in Year 5; using l × w × h (including cm³ and m³) is a Year 6 objective in England.

ME14 Telling the Time