What is the minimum thickness of a spherical shell that encloses the Earth's surface?
The two spheres are concentric, the outer sphere encloses all the surface (to the highest mountain), and the inner sphere excludes all the surface (down to the deepest ocean trench).
Yes, I know this is not strictly a mathematics question, but it is mathematical in some extended sense. Of course, just subtracting the highest mountain peak from the deepest ocean trench ignores the oblate spheroid shape of the Earth. I am curious to learn how close the Earth is to a sphere, and the shell thickness divided by, say, the inner radius, is one measure of that closeness. Thanks!