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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?

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Answer:

The correct answer is 0.0667 centimeters.

Step-by-step 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 [tex]\frac{12700}{35}[/tex] .

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 [tex]\frac{24.2}{x}[/tex] .

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

∴ [tex]\frac{12700}{35}[/tex] = [tex]\frac{24.2}{x}[/tex]

⇒ x = 0.0667 centimeters.

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