Volume of Liquids
Learn about litres, millilitres, and how they relate to cubic centimetres
1. Litres, Millilitres, and Cubic Centimetres
The Key Relationship:
1 litre = 1000 millilitres = 1000 cm³
1 ℓ = 1000 ml = 1000 cm³
Important Facts to Remember:
1 ml
=
1 cm³
1 ℓ
=
1000 ml
1 ℓ
=
1000 cm³
Why is this useful?
This allows us to calculate the volume of liquid a container can hold using the same formula as for solids!
Picturing 1 Litre:
10 cm × 10 cm × 10 cm cube
= 1000 cm³ = 1 ℓ
A cube measuring 10 cm along each edge can hold exactly 1 litre of water!
2. Converting Between Units
Conversion Guide:
cm³ → ml
Just use the same number!
100 cm³ = 100 ml
500 cm³ = 500 ml
1500 cm³ = 1500 ml
cm³ → ℓ
Divide by 1000 (from ℓ back to cm³, multiply by 1000)
1000 cm³ = 1 ℓ
2000 cm³ = 2 ℓ
3500 cm³ = 3.5 ℓ
Converting ml to ℓ and ml:
When there are 1000 ml or more, you can write the answer in litres and millilitres.
Example: 2310 ml = ?
2310 ml = 2000 ml + 310 ml
= 2 ℓ 310 ml
3. Volume of Water in Containers
How to Find the Volume of Water:
- Use the formula: Volume = length × breadth × height
- The height is the water level (how high the water is)
- Convert to ml or ℓ if needed
Example: Volume of Water in a Tank
A rectangular container measures 10 cm by 6 cm by 8 cm. It is completely filled with water. Find the volume of water in the container.
Solution:
Volume of water = length × breadth × height
= 10 cm × 6 cm × 8 cm
= 480 cm³
Since 1 cm³ = 1 ml:
Volume of water = 480 cm³ = 480 ml
Example: Converting to Litres and Millilitres
A rectangular tank measures 22 cm by 15 cm. Water fills it to a height of 7 cm. Find the volume of water. Give your answer in litres and millilitres.
Solution:
Volume of water = 22 cm × 15 cm × 7 cm
= 2310 cm³
= 2310 ml
Converting to litres and millilitres:
2310 ml = 2000 ml + 310 ml
Volume of water = 2 ℓ 310 ml
Practice Problems
Practice 1: Convert to ml
Express 69 cm³ in millilitres.
ShowHide solution
Since 1 cm³ = 1 ml:
69 cm³ = 69 ml
Practice 2: Convert Litres to cm³
Express 7 ℓ in cubic centimetres.
ShowHide solution
Since 1 ℓ = 1000 cm³:
7 ℓ = 7 × 1000 = 7000 cm³
Practice 3: Convert to ℓ and ml
Express 8034 ml in litres and millilitres.
ShowHide solution
8034 ml = 8000 ml + 34 ml
= 8 ℓ 34 ml
Practice 4: Volume of Water
A rectangular tank measures 20 cm by 20 cm by 25 cm. It is completely filled with water. Find the volume of water. Give your answer in litres.
ShowHide solution
Volume = 20 cm × 20 cm × 25 cm = 10000 cm³
= 10000 ml
10000 ÷ 1000 = 10, so the volume of water is 10 ℓ
Key Takeaways
- 1 ml = 1 cm³ (they are the same!)
- 1 ℓ = 1000 ml = 1000 cm³
- To convert cm³ to ml: use the same number
- To convert cm³ to ℓ: divide by 1000; to convert ℓ to cm³: multiply by 1000
- In a rectangular tank: volume of liquid = length × breadth × height of the water
- Express large volumes in ℓ and ml (e.g., 2 ℓ 310 ml)