Steel expands 11 parts in a million for each 1 degree C change. Consider a 40,000 km steel pipe that forms a ring to fit snugly all around the circumference of the Earth. Suppose people along its length breathe on it so as to raise its temperature 0.80 degree C. The pipe gets longer. It also is no longer snug. How high does it stand above ground level? (To simplify, consider only the expansion of its radial distance from the center of Earth, and apply the geometry formula that relates circumference C and radius r, C = 2 \pi r. The result is surprising!)

To find out how high the pipe stands above the ground level, we need to consider the expansion of its radial distance from the center of the Earth. Since the pipe forms a ring that fits snugly around the Earth, we can assume its initial radius is equal to the Earth's radius.

Let's break down the problem and calculate step by step:

1. Calculate the initial radius of the pipe: Since the pipe fits snugly around the Earth, its initial radius is equal to the Earth's radius, which is approximately 6,371 km (or 6,371,000 meters).

2. Calculate the expansion of the radius due to the temperature change: We know that for every 1 degree Celsius change, the steel expands 11 parts in a million. So, for a temperature increase of 0.80 degrees Celsius, the expansion of the steel can be calculated as:
Expansion = (Initial Radius) * (Expansion Coefficient) * (Temperature Change)
= (6,371,000 meters) * (11/1,000,000) * (0.80 degrees Celsius)

3. Calculate the new radius after expansion: To find the new radius of the pipe after expansion, we add the expansion to the initial radius.
New Radius = Initial Radius + Expansion

4. Calculate the new circumference of the pipe: The circumference of a circle can be calculated using the formula C = 2 * π * r, where r is the radius of the circle.
New Circumference = 2 * π * New Radius

5. Calculate the change in height: The change in height is the difference between the new circumference of the pipe and the circumference of the Earth (which is also equal to 2 * π * Earth's Radius).
Change in Height = New Circumference - Circumference of Earth

Finally, let's calculate the result:

Initial Radius = 6,371,000 meters
Expansion Coefficient = 11/1,000,000
Temperature Change = 0.80 degrees Celsius
New Radius = Initial Radius + (Initial Radius) * (Expansion Coefficient) * (Temperature Change)
New Circumference = 2 * π * New Radius
Change in Height = New Circumference - (2 * π * Earth's Radius)

By substituting the values, you can calculate the height the pipe stands above the ground level based on the given parameters.