📦 Volume

Count cubes, calculate cuboids, find missing dimensions!

📖 Learn
Volume concepts
✏️ Examples
Worked problems
🔬 Visualiser
Interactive tools
🎯 Practice
20 mixed questions

📖 Volume

1. What is Volume?

Volume is the amount of 3D space an object takes up. We measure it in cubic units: cm³, m³, mm³.

Think of filling a box with unit cubes — the number of cubes is the volume!

Volume = number of unit cubes that fit inside

2. Volume of a Cuboid

A cuboid (rectangular box) has length, width and height.

V = length × width × height
V = l × w × h

Units: if l, w, h are in cm → V is in cm³

If l, w, h are in m → V is in

3. Volume of a Cube

A cube has equal sides. If the side length is s:

V = s × s × s = s³

Example: cube with side 4 cm → V = 4³ = 64 cm³

4. Finding a Missing Dimension

If you know the volume and two dimensions, divide to find the third:

l = V ÷ (w × h)

Example: V = 120 cm³, w = 5 cm, h = 4 cm
l = 120 ÷ (5 × 4) = 120 ÷ 20 = 6 cm

5. Units of Volume

UnitUsed forConversion
mm³tiny objects1 cm³ = 1000 mm³
cm³everyday objects1 litre = 1000 cm³
rooms, buildings1 m³ = 1,000,000 cm³

Key link: 1 ml = 1 cm³ (used in capacity)

✏️ Worked Examples

Example 1 – Cuboid volume

Find the volume of a cuboid: length 8 cm, width 5 cm, height 3 cm.

V = l × w × h
V = 8 × 5 × 3
V = 40 × 3 = 120 cm³

Example 2 – Cube volume

Find the volume of a cube with side length 6 cm.

V = s³ = 6 × 6 × 6
6 × 6 = 36
36 × 6 = 216 cm³

Example 3 – Missing dimension

A cuboid has volume 180 cm³, length 9 cm, height 4 cm. Find the width.

V = l × w × h → w = V ÷ (l × h)
w = 180 ÷ (9 × 4) = 180 ÷ 36
w = 5 cm

Example 4 – Word problem with units

A fish tank is 50 cm long, 25 cm wide and 30 cm tall. How many litres of water does it hold when full? (1 litre = 1000 cm³)

V = 50 × 25 × 30 = 37 500 cm³
Litres = 37 500 ÷ 1000 = 37.5 litres

🔬 Volume Visualiser

Cuboid Calculator






Find Missing Dimension






Unit Converter




Exercise 1 – Cuboid Volume

Calculate the volume of each cuboid. Give units.

Exercise 2 – Cube Volume

Find the volume of each cube.

Exercise 3 – Missing Dimensions

Find the missing measurement.

Exercise 4 – Units & Conversions

Convert between units or complete the statement.

Exercise 5 – Word Problems

Solve each problem.

🎯 Practice – 20 Questions

🏆 Challenge