Units of Area and Volume – Questions Answered | Pearson Edexcel International GCSE Maths

These examples practise converting units of area and volume, using powers of 10, writing values in standard form, and applying the pressure formula. Particular care is needed because area conversions are squared and volume conversions are cubed.

Question 1(a) – Converting m² to cm²

Convert 2.3 m² into cm².

Working

Convert 2.3 m² into cm².

1 m = 10² cm

2.3 × (10² cm)²

= 2.3 × 10⁴ cm²
Answer: 2.3 × 10⁴ cm²

Question 1(b) – Converting mm³ to cm³

Convert 400 mm³ into cm³.

Working

Convert 400 mm³ into cm³

10 mm = 1 cm
1 mm = 10⁻¹ cm

400 × (10⁻¹ cm)³

= 400 × 10⁻³ cm³

= 4 × 10² × 10⁻³ cm³

= 4 × 10⁻¹ cm³
Answer: 4 × 10⁻¹ cm³

Question 2 – Converting Cubic Metres to Cubic Millimetres

Convert 0.35 m³ into mm³, giving the answer in standard form.

Working

Convert 0.35 m³ to mm³
giving your answer in standard form.

1 m = 10³ mm
(1 m)³ = (10³ mm)³
1 m³ = 10⁹ mm³

0.35 m³

= 3.5 × 10⁻¹ × 10⁹ mm³

= 3.5 × 10⁸ mm³
Answer: 3.5 × 10⁸ mm³

Why the Conversion Factor Must Be Squared or Cubed

A linear conversion applies to one dimension. When an area is converted, the conversion factor applies to two dimensions, so it must be squared.

1 m = 10² cm

1 m² = (10²)² cm² = 10⁴ cm²

For volume, the conversion factor applies in three dimensions, so it must be cubed.

1 m = 10³ mm

1 m³ = (10³)³ mm³ = 10⁹ mm³

Question 3 – Pressure

A person applies a force of 600 N to the floor. The total area of contact is 160 cm². Find the pressure in N/m².

Working

P = F / A

F = 6 × 10² × N
A = 1.6 × 10² × cm²

1 cm = 10⁻² m
(1 cm)² = (10⁻² m)²
1 cm² = 10⁻⁴ m²

P = (6 × 10² × N) / (1.6 × 10² × 10⁻⁴ m²)

= (6 × 10² × N) / (1.6 × 10⁻² × m²)

= (6 / 1.6) × 10⁴ × N/m²

= 3.75 × 10⁴ × N/m²
Answer: 3.75 × 10⁴ N/m²

Key Results

2.3 m² = 2.3 × 10⁴ cm²

400 mm³ = 4 × 10⁻¹ cm³

0.35 m³ = 3.5 × 10⁸ mm³

P = 3.75 × 10⁴ N/m²

Source: Questions adapted from Harry Smith, Revise Pearson Edexcel International GCSE (9–1) Mathematics A – Higher Tier Revision Guide, Pearson.

Solutions and workings: Tiago Hands.

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