Question

The Earth’s total diameter is 12700 kilometers, with the solidified, ocean-covered crust that is at its thickest 35 kilometers wide. These massive sizes and the difference between them may be hard to imagine, so scale-model globes of the Earth shrink our tremendous planet down to a more manageable size. If the Earth’s diameter was shrunken to the size of a basketball (24.2 centimeters across), how thick would the Earth’s crust be in this model Earth, in centimeters?

Answer 1

The correct answer is 0.0667 centimeters.

Explanation:

Diameter of earth is 12700 kilometers.

Width of the solidified ocean crust is 35 kilometers.

Ratio between the diameter of the earth and the solidified crust is
`(12700)/(35)` .

Now the earth is shrunken to a size of a basketball with the diameter as 24.2 centimeters. Let the thickness of the Earth's crust in this model be x centimeters.

Ratio between the diameter of the model earth and the solidified crust is
`(24.2)/(x)` .

But this ratio of the real Earth and its model must be equal.

∴
`(12700)/(35)` =
`(24.2)/(x)`

⇒ x = 0.0667 centimeters.