Quick answer: When length units change by a factor k, area changes by k² and volume by k³. Thus 1 m = 100 cm, 1 m² = 10,000 cm² and 1 m³ = 1,000,000 cm³.
Worked example
Convert 2.5 m² to cm² and 0.004 m³ to litres.
- For area, multiply by 100²: 2.5×10,000 = 25,000 cm².
- For volume, 1 m³ = 1,000 litres.
- Therefore 0.004 m³ = 4 litres.
- Equivalently this is 4,000 cm³ because 1 litre = 1,000 cm³.
Check the result
A cube of side 1 m contains 100×100×100 cubes of side 1 cm.
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Common mistake to avoid
Multiplying square metres by only 100 is incorrect. Keep units written at each step and convert all dimensions before using a formula.
Try it yourself
1. Convert 300 cm² to m². 2. Convert 2 litres to cm³.
Answers and reasoning
1. 300/10,000 = 0.03 m². 2. 2×1,000 = 2,000 cm³.
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