Saturday, October 30, 2021

Problem. Is it possible that the displaced volume of the liquid exceeds the total volume of the liquid?

In a vertical cylindrical vessel with a radius of 4.37 cm, a liquid with a density of 1.00 g / cm³ have been poured. The height of the liquid level above the bottom of the vessel is 5.00 cm.

A homogeneous vertical cylinder with a radius of 4.01 cm and a height of 10.00 cm is lowered into the vessel.

The density of the cylinder material is 0.99 g / cm³.

No liquid spills.

1) What is the volume of liquid in the vessel?

2) How (quantitatively) will the liquid level in the vessel change?

3) Will the cylinder float in liquid without touching the bottom?

4) If the cylinder floats in the liquid without touching the bottom, then how much volume of liquid is the displaced by cylinder, in accordance with Archimedes' law?