Question

If every person in the world were to own an equal share of the earth’s land, how many square miles would each person have? You may assume the earth is a sphere with a radius is 3959 miles and that 20 percent of its surface is land suitable to live on. There are approximately 7.7 billion people on earth as of 2019.

1. Given the earth’s surface area that is suitable to live on, the area that will be owned by each person on earth is approximately 5.12 × 10⁻³ mi² per person.

How many square miles would each person have?

The earth has a spherical shape. The surface area of a sphere is measured using the equation;
A = 4πr²
Where r is radius and π is constant pi ( π = 3.14 )
Given the data in the question;
• Radius of earth r = 3959 miles
• Percentage of earth suitable to live = 20%
• Number of people on earth = 7.7 billion = 7.7 × 10⁹
First we calculate, the surface area of the earth.
A = 4πr²
A = 4 × 3.14 × ( 3959 mi )²
A = 4 × 3.14 × ( 3959 mi )²
A = 1.97 × 10⁸mi²
Next, we calculate the percentage of the earth surface that is suitable to live on.
20% of surface area
20% of 1.97 × 10⁸mi²
20/100 × 1.97 × 10⁸mi²
3.94 × 10⁷mi²
The percentage of the earth surface that is suitable to live on is 3.94 × 10⁷mi²
Next we divide the suitable surface area by the number of people on earth.
= ( 3.94 × 10⁷mi² ) ÷ ( 7.7 × 10⁹ )
= 5.12 × 10⁻³ mi² per person
Given the earth’s surface area that is suitable to live on, the area that will be owned by each person on earth is approximately 5.12 × 10⁻³ mi² per person.