Who does all the calculation in Archimedes Principle? [closed]

Question

Let's do an experiment.

In the first half of the experiment, you ask some geometers to determine the volume of a pineapple. They would model the 3D shape of the pineapple, which is a pretty tricky task, and then proceed to calculate the volume. Even if they use some computer software and approximate some parts of the pineapple, the amount of calculation involved would still be pretty large.

Now hand over the pineapple to Archimedes for the second half of the experiment. He would immerse it in a water tub, collect the overflow water and measure the volume with a cylinder. The only calculation that he does is multiply the base area of the cylinder with the height of the water column. That is so easy! Compare that with the hardship the geometers had to go through!

This is what amuses me. How can a complex problem become trivial just because the object is immersed in water?

More precisely, the geometers are the ones who did all the calculations for the first half of the experiment. Who is doing all those math in the second half?

Answer 1

Who does all the calculation in Archimedes Principle?

All of the tiny little water molecules.

They are all jostling for position inside the cylinder. The ones that can no longer fit due to the pineapple taking up space end up in the overflow - it's like a gigantic game of musical chairs. And by measuring the volume of the overflow you are, in effect, counting the water molecules that cannot find a "chair" and are out. And that tells you how many "chairs" the pineapple has taken up.