Question

the habitable part of earth’s surface has been estimated to cover 60 trillion square meters. estimate the percent of this area occupied by humans if earth’s current population stood packed together as people do in a crowded elevator. options: 10⁻³%, 10⁻¹%, 10%, 50%

Explanation:

Step1: Recall Earth's population and personal space

Assume Earth's population is about \( 8\times10^{9} \) people. In a crowded elevator, a person occupies about \( 0.1 \, \text{m}^2 \) (so \( 10 \, \text{people/m}^2 \), but let's use \( 0.1 \, \text{m}^2 \) per person for simplicity).

Step2: Calculate total area occupied by humans

Total area \( A = \text{population} \times \text{area per person} \).
\( A = 8\times10^{9} \times 0.1 = 8\times10^{8} \, \text{m}^2 \).

Step3: Calculate the percentage

Habitable area \( H = 60\times10^{12} \, \text{m}^2 \) (60 trillion).
Percentage \( \% = \frac{A}{H} \times 100 = \frac{8\times10^{8}}{60\times10^{12}} \times 100 \).
Simplify: \( \frac{8}{60\times10^{4}} \times 100 = \frac{8}{6\times10^{5}} \approx 1.33\times10^{-5}\% \approx 10^{-3}\% \) (since \( 10^{-3}\% = 0.001\% \), and our calculation is ~0.000133%, close to \( 10^{-3}\% \) in order of magnitude).

Answer:

\( 10^{-3}\% \) (the option \( 10^{-3}\% \))