Final answer:
On a basketball-sized Earth (24 cm in diameter), the Earth's crust would be significantly thinner than the leather covering of the basketball, roughly equivalent to the thickness of a line drawn with a ballpoint pen.
Step-by-step explanation:
Let's consider the Earth's size in relation to a basketball to understand the thickness of the Earth's crust. A basketball has a diameter of about 24 centimeters. Since the average thickness of the Earth's crust is 35 kilometers on land and 5–6 kilometers under the oceans, we need to use a scale to find out its equivalent on a basketball-sized Earth.
Using a scale factor of 1 billion (109), as we do when we build scale models, we can calculate the crust's thickness. The actual Earth's diameter is approximately 12,700 kilometers, so if Earth is scaled down to 24 centimeters, we divide both the actual diameter and crust's thickness by the same factor. At this scale, 1 kilometer is represented by 24 centimeters / 12,700 kilometers = 0.00188976 centimeters.
Now, let's calculate the scale thickness of the Earth's crust on a basketball-sized Earth:
- The thickness of the land crust would be 35 km * 0.00188976 cm/km ≈ 0.066 centimeters.
- The thickness of the oceanic crust would be 5.5 km (average) * 0.00188976 cm/km ≈ 0.0104 centimeters.
Therefore, if the Earth was the size of a basketball, the crust would be about the thickness of a line drawn with a ballpoint pen, significantly less than the thickness of the basketball's leather covering.