The Human Cube™ (1)

Classical Mechanics Level 2

If we were to put everyone in the world in a massive cube then how long would a side of that cube be?

Take 8 billion people as a rough measurement and 60 kg as a rough weight. Assume there are no gaps between the people - nor is there any 'compression' of anyone. Human density ≈ \approx Water density.

4,800 kilometers 783,000 kilometres 4.8 kilometres 48 kilometers 783 metres

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

Chew-Seong Cheong
Feb 16, 2020
  • Total mass of 8 billion people, M = 8 × 1 0 9 × 60 = 480 × 1 0 9 kg M = 8 \times 10^9 \times 60 = 480 \times 10^9 \text{ kg} .
  • Density of human, ρ human ≈ ρ water = 1 0 3 kg/m 3 \rho_{\text{human}} \approx \rho_{\text{water}} = 10^3 \text{ kg/m}^3 .
  • Volume of the massive cube, V = M / ρ human ≈ 480 × 1 0 9 / 1 0 3 = 480 × 1 0 6 m 3 V = M/\rho_{\text{human}} \approx 480 \times 10^9 / 10^3 = 480 \times 10^6 \text{ m}^3 .
  • Side length of the massive cube, a = V 3 = 480 × 1 0 6 3 ≈ 783 m a = \sqrt [3] V = \sqrt[3]{480 \times 10^6} \approx \boxed{\text{783 m}} .
1 Helpful 0 Interesting 1 Brilliant 0 Confused
Steven Chase
Feb 16, 2020 
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import math

m = 60.0                # individual human mass
N = 8.0*(10.0**9.0)     # number of humans
rho = 1000.0            # water density

M = m*N                 # total human mass

V = M/rho               # total human volume

S = V**(1.0/3.0)        # cube side length

print S
# 782.973528234

1 Helpful 0 Interesting 1 Brilliant 0 Confused

Great. How do you insert this ^ table?

A Former Brilliant Member - 1 year, 3 months ago

Thanks. It is Python code. Brilliant allows code entry

Steven Chase - 1 year, 3 months ago

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