Maths Unit Conversion Guide | Cambridge IGCSE

Maths Unit Conversion Guide

Cambridge IGCSE Mathematics 0580 Syllabus - Mensuration (E5.1)

Key Conversion Rules

Length

1 km = 1000 m
1 m = 100 cm
1 cm = 10 mm

Area

1 m² = 10,000 cm²
1 cm² = 100 mm²

Volume/Capacity

1 m³ = 1000 litres
1 litre = 1000 cm³
1 cm³ = 1 ml

Mass

1 kg = 1000 g

Worksheet Examples

1. Cylindrical Volume (CD Q1)

Question: Radius = 14.2 cm, Height = 18 cm → Volume in cm³ and litres.

Solution:

Volume = πr²h = π × (14.2)² × 18 ≈ 11400 cm³
Convert to litres: 11400 cm³ = 11.4 litres

2. Cuboid Water Tank (CD Q4)

Question: Length = 1.5 m, Width = 1 m, Depth = 60 cm → Volume in litres.

Solution:

Convert depth to metres: 60 cm = 0.6 m
Volume = 1.5 × 1 × 0.6 = 0.9 m³
Convert to litres: 0.9 × 1000 = 900 litres

3. Pipe Flow Rate (AB Q3)

Question: Pipe radius = 1.5 cm, speed = 8 cm/s → Water flow in 1 hour (litres).

Solution:

Cross-section area = πr² = π × (1.5)² ≈ 7.07 cm²
Volume per second = 7.07 × 8 = 56.56 cm³/s
Hourly volume = 56.56 × 3600 = 203,616 cm³ = 203.6 litres

SI Prefixes Reference Table

Prefix	Symbol	Multiplier	Example
Tera	T	10¹²	1 TB = 10¹² bytes
Giga	G	10⁹	1 GHz = 10⁹ Hz
Mega	M	10⁶	1 MW = 10⁶ watts
Kilo	k	10³	1 km = 1000 m
Milli	m	10⁻³	1 mm = 0.001 m
Micro	μ	10⁻⁶	1 μm = 10⁻⁶ m
Nano	n	10⁻⁹	1 nm = 10⁻⁹ m
Pico	p	10⁻¹²	1 pF = 10⁻¹² farads

Practice Quiz

Question 1

Convert 6450 cm to metres.

Question 2

Change 7850 cm³ to litres.

Question 3

A cone has radius 8 cm, slant height 17 cm. Find its curved surface area (use πrl).

Question 4

Which is larger: 84,000 cm³ or 0.1 m³?

Question 5

A parcel has dimensions 18 cm × 10 cm × 8 cm. Find its volume in cm³.

Quiz Answers

64.5 m
7.85 litres
π × 8 × 17 = 136π cm²
0.1 m³ = 100,000 cm³ → So 0.1 m³ is larger
18 × 10 × 8 = 1440 cm³

Exam Tips

Always convert units to the same type before calculating
Remember: 1 m³ = 1000 litres, 1 cm³ = 1 ml
For flow rates, find volume per second first, then multiply by time
Double-check your conversions in multi-step problems
Pay attention to significant figures in your final answers