Question

We hear a great deal about overpopulation, but if air and elbow room were not an issue, show that you could put the entire world population of humans, 7 billion people, into a cube 1 mile x 1 mile x 1 mile. Assume, on average, people can fit into a box that is 7' tall, 2' wide and 1' deep.

Answer 1

Answer: The below explanation shows that we could put the entire population on the given box.

Explanation:

Here, it is given that on average, people can fit into a box that is 7' tall, 2' wide and 1' deep.

That is, the approximate volume of the box in which a person can be fit = 7 × 2 × 1 = 14 cube feet

But, the given population of the world = 7 000,000,000

Thus, the total approximate volume of the 7 billion people = 14 × 7 000,000,000 = 98,000,000,000 cube feet

Also, it is given that, the volume of the given box = 1 mile x 1 mile x 1 mile =
`5280^3` cube feet = 147197952000 cube feet.

Since, we can say that the entire population of the world can put the box

If total volume of the box / total volume of the population
`\geq` 1

Here, 147197952000 / 98,000,000,000 = 1.5 > 1

Therefore, the entire population can be put in the box.