If all the people in the world are crowded together in one location, how much area would it cover?
Answer: About 8.2 billion people at about 4 people per m2 (0.25 m2 each) need about 2.05 × 109 m2 ≈ 2000 km2: a square only about 45 km on each side.
Step-by-step solution
Idea: Area needed = number of people × floor space for one standing person. A tightly packed crowd has about 4 people per square metre.
- Guess first, then assume: world population ≈ 8.2 billion = 8.2 × 109; each person standing closely needs about 0.5 m × 0.5 m = 0.25 m2.1 mark
- Area = 8.2 × 109 × 0.25 = 2.05 × 109 m2. Since 1 km2 = 106 m2, this is about 2050 km2.1 mark
- √2050 ≈ 45, so everyone fits in a square about 45 km × 45 km, roughly the size of one large city.1 mark
About 2000 km² (a square about 45 km on each side), assuming 8.2 billion people at 0.25 m² each.
Check: 45 km × 45 km = 2025 km2 ≈ 2050 km2 ✓.
Answer to write in the exam
Population ≈ 8.2 × 109; space per person ≈ 0.25 m2
Area = 8.2 × 109 × 0.25 = 2.05 × 109 m2
= 2050 km2 (1 km2 = 106 m2)
∴ About 2000 km2, a square about 45 km per side
Common mistakes that cost marks
- Converting m2 to km2 by dividing by 1000 instead of 106.
- Using a whole room or house for each person, which is not ‘crowded together’.
How this can come in the exam
MCQ (1 mark)
1 km2 equals
- 1000 m2
- 10 000 m2
- 1 000 000 m2
- 100 m2
Show answer
(C) 1 000 000 m2
1000 m × 1000 m = 106 m2.
Try one yourself
A stadium crowd of 60,000 people stands 4 per m2. What area do they need?
Show answer
60,000 × 0.25 = 15,000 m2 (about 2 football fields).
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