How does archimedes’ principle explain how much fluid is displaced by an object?

The amount of fluid displaced by an object doesn't really
need to be explained.

Whenever you drop or stick something into a fluid, it just
pushes as much fluid out of its way as it needs to.  That's
just the volume of the object ... or the volume of as much
of the object as sinks into the fluid.

If the whole object goes into the fluid, then the volume of
fluid displaced is equal to the volume of the object.

If the object comes to the end of its string and stops descending,
or the buoyant force holding it up becomes equal to its weight and
it stops descending, then the volume of fluid displaced is equal to
however much volume of the object went into the fluid.  It doesn't 
take Archimedes to explain that to us. 

What Archimedes discovered is how to tell what the buoyant force
holding the object up is going to be, once it starts entering the fluid.
THAT's going to be the weight of however much fluid it displaces.

Year  1936,  lehman predicted that the earths 'inner core' is solid. she observed that the seismic signals during her study were bent and did not pass through instead bouncing back. later it was confirmed that the earth's inner core was solid made up of nickel-iron and had a molten outer core.