Volume - Measuring Three-Dimensional Space
Volume is the amount of three-dimensional space that an object or substance occupies. It is one of the most widely used measurements – from calculating how much concrete to pour, to filling a swimming pool, to packaging a product.
Volume vs Capacity
Volume refers to the space taken up by any solid, liquid, or gas.
Capacity is the maximum volume a container can hold, usually for liquids.
The key link: 1 ml = 1 cm³, so volume and capacity share the same numerical value in these units.
Units of Volume
| Unit | Symbol | Typical use |
|---|---|---|
| Cubic millimetre | mm³ | Very small objects |
| Cubic centimetre | cm³ | Small solids, medicine (1 cm³ = 1 ml) |
| Cubic metre | m³ | Large spaces such as rooms and concrete pours |
| Millilitre | ml | Liquids (1 ml = 1 cm³) |
| Litre | l | Liquids (1 l = 1,000 cm³) |
Volume Conversion Table
| Conversion | Operation |
|---|---|
| cm³ to ml | 1:1 (same value) |
| ml to l | ÷ 1,000 |
| l to ml | × 1,000 |
| m³ to litres | × 1,000 |
| cm³ to m³ | ÷ 1,000,000 |
Key Volume Formulas
| Solid | Formula |
|---|---|
| Cube | V = s³ |
| Cuboid | V = l × w × h |
| Cylinder | V = πr²h |
| Cone | V = ⅓πr²h |
| Sphere | V = &frac43;πr³ |
| Any prism | V = cross-section area × length |
Worked Examples
A storage box is 50 cm x 40 cm x 30 cm. Find its volume in litres.
V = 50 × 40 × 30 = 60,000 cm³ = 60,000 ml = 60 litres.
A cylindrical tank has radius 0.5 m and height 2 m. Find its volume in litres.
V = π(0.5)²(2) = 0.5π ≈ 1.571 m³. 1.571 × 1,000 = 1,571 litres.
Convert 3.5 m³ to litres.
3.5 × 1,000 = 3,500 litres.
Key Takeaways
- Volume measures 3D space in cubic units or litres and millilitres.
- 1 cm³ = 1 ml | 1 litre = 1,000 cm³ | 1 m³ = 1,000 litres.
- For any prism: V = cross-section area × length.
Practice Questions
- Find the volume in litres of a cuboid 80 cm x 50 cm x 25 cm.
- A sphere has radius 6 cm. Find its volume. Leave in terms of π.
- Convert 4.2 m³ to litres.
- A cylinder has diameter 10 cm and height 15 cm. Find its volume to 2 decimal places.
- A swimming pool is 25 m long, 10 m wide and 2 m deep. How many litres does it hold?