A little thought experiment for those that don't wish to remain thoughtless...

[Guest guest]

Here's something that ran through my mind a few years ago, at least

the general idea. Let's go on the basis that we have a construction

team that can build a shallow pool 1 inch deep and 100 miles in

diameter, with it being perfectly placed, with the bottom perfectly

flat and level at the mathematical center of the circular pool, with

the bottom of the pool a precise mathematical plane (zero

imperfections: *perfectly* flat, and the center exactly tangent with

the diameter of the center of earth).

Now here is where things get entertaining: think about what will

happens when you fill the pool with exactly the volume of water to

cover a 100 mile diameter circle 1 inch deep with exactly that volume

of water as given by the volume formula for that cylinder (ie. 1 inch

high, 100 miles in diameter). Please note I'm not asking for the

actual volume of water, and the dimensions given are purely arbitrary:

the real dimensions (until you get to a small enough scale) are

irrelevant to this discussion, not affecting the outcome.

What is the final result, and why is that? (note I already have the

answer)