Volume in Cubic Centimetres and Cubic Metres
Learn about standard units of volume: cm³ and m³
1. Cubic Centimetres (cm³)
What is a 1-cm cube?
A 1-cm cube is a cube where each edge is exactly 1 centimetre long.
This is a 1-cm cube.
Volume of a 1-cm cube:
Volume = 1 cubic centimetre = 1 cm³
Building with 1-cm cubes:
• A solid made of 6 of these 1-cm cubes has volume 6 cm³
• A solid made of 8 of these 1-cm cubes has volume 8 cm³
• A solid made of 12 of these 1-cm cubes has volume 12 cm³
When to use cm³: For small objects like erasers, dice, sugar cubes, or small containers.
2. Cubic Metres (m³)
What is a 1-m cube?
A 1-m cube is a cube where each edge is exactly 1 metre long.
This is a 1-m cube. Each edge is as long as a metre ruler.
Volume of a 1-m cube:
Volume = 1 cubic metre = 1 m³
Building with 1-m cubes:
• A solid made of 8 of these 1-m cubes has volume 8 m³
• A solid made of 18 of these 1-m cubes has volume 18 m³
• A solid made of 24 of these 1-m cubes has volume 24 m³
When to use m³: For large objects like rooms, swimming pools or shipping containers.
3. Choosing the Right Unit
Use cm³ for:
- 📦 Small boxes
- 🧊 Ice cubes
- 🎲 Dice
- 🍬 Sweet tins
- 📚 Small books
Use m³ for:
- 🏠 Rooms
- 🏊 Swimming pools
- 📦 Shipping containers
- 🚛 Lorries
- 🏢 Buildings
Think About It:
How many 1-cm cubes can fit inside a 1-m cube?
1 m = 100 cm, so a 1-m cube is 100 cm × 100 cm × 100 cm
That's 100 × 100 × 100 = 1,000,000 of the 1-cm cubes!
Worked Example
Example: Finding Volume in cm³
A solid is built using 1-cm cubes. It has 3 layers, with 2 rows of 4 cubes in each layer. Find its volume in cm³.
Solution:
Step 1: Cubes in one row = 4
Step 2: Cubes in one layer = 4 × 2 = 8 cubes
Step 3: Total cubes = 8 × 3 = 24 cubes
Volume = 24 cm³
Practice Problems
Practice 1: Volume in cm³
I use 15 of the 1-cm cubes to build a solid. What is its volume?
ShowHide solution
Each 1-cm cube has a volume of 1 cm³, so the volume is 15 cm³
Practice 2: Volume in m³
A cuboid is made of 1-m cubes. It has 2 layers. Each layer has 3 rows of 4 cubes. What is its volume?
ShowHide solution
Cubes in one layer = 3 × 4 = 12 cubes. Total cubes = 12 × 2 = 24 cubes, so the volume is 24 m³
Practice 3: Choosing Units
Which unit (cm³ or m³) would you use to measure the volume of: (a) a pencil box, (b) a classroom?
ShowHide solution
(a) Pencil box: cm³ (small object)
(b) Classroom: m³ (large space)
Key Takeaways
- A 1-cm cube has a volume of 1 cm³ (1 cubic centimetre)
- A 1-m cube has a volume of 1 m³ (1 cubic metre)
- Use cm³ for small objects (erasers, dice, pencil boxes)
- Use m³ for large objects (rooms, pools, buildings)
- Count the cubes to find the volume in the correct unit