Volume: a concept of space

What is volume?

Volume measures the space occupied by a solid (a three-dimensional object). Unlike area, which measures a flat surface in cm² or m², volume is expressed in cubic units: cm³, m³, dm³, etc.

You can think of volume as the number of small cubes, each with a side length of 1 cm, that would be needed to completely fill a solid.

Units of volume

Units of volume are organised in multiples of 1,000 (as there are three dimensions: length × width × height):

Unit	Equivalence
1 m³	1,000 dm³
1 dm³	1,000 cm³
1 cm³	1,000 mm³

Key point: 1 dm³ = 1 litre (L). This is very useful for relating volumes to liquid capacities.

Practical example

A 1 m³ aquarium contains 1,000 dm³ of water, or 1,000 litres.

Common pitfall to avoid

Don’t confuse area conversions (factor of 100) with volume conversions (factor of 1000)!

• 1 m² = 100 dm² (area)
• 1 m³ = 1,000 dm³ (volume)

Many pupils forget this factor of 1,000 and mistakenly use 100 instead. Always remember to count all three dimensions.