The Human Cube™ (2)

Classical Mechanics Level 2

The air has become toxic, but humans can now swim underwater! Using The Human Cube™ (1) how much would sea level rises if the whole world of around 8 billion people went swimming? The Human Cube™ has a side length of ≈ \approx 783 metres. The surface area of water is 362 million square kilometres.

0.2 km 1.3 μm (micrometers) 0.2 cm 80 nm (nanometers) 1.3 km

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2 solutions

Chew-Seong Cheong
Feb 17, 2020
  • The human cube is V = 78 3 3 ≈ 480 × 1 0 6 m 3 V = 783^3 \approx 480 \times 10^6 \text{ m}^3 .
  • The total seawater surface area is A = 362 × 1 0 6 (km) 2 = 362 × 1 0 6 × 1 0 6 m 2 = 362 × 1 0 12 m 2 A = 362 \times 10^6 \text{ (km)}^2 = 362 \times 10^6 \times 10^6 \text{ m}^2 = 362 \times 10^{12} \text{ m}^2 .
  • The rise in sea level is h = V A = 480 × 1 0 6 362 × 1 0 12 ≈ 1.3 × 1 0 − 6 m = 1.3 μ m h = \dfrac VA = \dfrac {480 \times 10^6 }{362 \times 10^{12}} \approx 1.3 \times 10^{-6} \text{ m} = \boxed{1.3\ \mu\text m} .
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