Sheet № 233 · Foundation + Higher · AQA · Edexcel · OCR
Converting Area and Volume Units –
Converting area and volume units trips up many GCSE Maths students because the conversion factors are not the same as for length. While 1 m = 100 cm for length, 1 m² = 10,000 cm² for area and 1 m³ = 1,000,000 cm³ for volume. Understanding why these factors are squared or cubed is the key to getting these questions right every time. This t
§Key definitions
Question:
Convert 3.5 m² to cm².
Answer:
3.5 m² = 35,000 cm².
Q1 (Foundation):
Convert 50,000 cm² to m².
Q2 (Foundation):
Convert 2.5 litres to cm³.
Q3 (Higher):
A swimming pool has a volume of 72 m³. How many litres of water does it hold?
§Formulas to memorise
1 m² = 10,000 cm² (because 100 x 100 = 10,000)
1 km² = 1,000,000 m² (because 1000 x 1000 = 1,000,000)
1 cm² = 100 mm² (because 10 x 10 = 100)
1 m³ = 1,000,000 cm³ (because 100 x 100 x 100 = 1,000,000)
1 cm³ = 1 ml
1 litre = 1,000 cm³ = 1,000 ml
Worked example
Convert 3.5 m² to cm².
Working:
⚠ Common mistakes
- ✗Using the length conversion factor for area or volume. Converting 2 m² to cm² is NOT 2 x 100 = 200 cm². It is 2 x 10,000 = 20,000 cm². You must square the factor for area and cube it for volume.
- ✗Multiplying when you should divide (or vice versa). Going from a small unit to a large unit means fewer of the large unit, so divide. Going from large to small means more of the small unit, so multiply.
- ✗Confusing cm³ and litres. Remember: 1 litre = 1,000 cm³, and 1 cm³ = 1 ml. These are essential for volume questions in context.
- ✗Forgetting that 1 m³ is a very large volume. 1 m³ = 1,000 litres. Students sometimes underestimate this.
✦ Exam tips
- →Draw a quick diagram of a 1 m x 1 m square labelled in centimetres if you forget the factor. This instantly shows you that 1 m² = 10,000 cm².
- →Write out the conversion chain: "1 m = 100 cm, so 1 m² = 100² cm² = 10,000 cm²." This earns method marks.
- →For volume questions involving capacity (litres), always convert to cm³ first if the dimensions are given in cm.
- →At Higher tier, these conversions often appear inside compound measure problems (e.g., converting density from g/cm³ to kg/m³).