I don't understand Archimedes principle

[lionely]

Homework Statement

The problem is I have about 13 questions to do, but I don't understand Archimedes principle when my teacher was supposed to teach it at school, all he did was send notes...
I do extra classes for Physics, the teacher there taught it, I understand a little better, but still not to the extent I want to, the teacher gave homework, the questions are quite difficult quoting him " These questions can kill a cow." So I was wondering if someone here could explain it at a Grade 11 level.

 

[SteamKing]

Archimedes principle! You could look it up!

A floating body displaces an amount of fluid equal to the weight of the body.

 

[LawrenceC]

If you have already learned how to calculate pressure under water, here is a simple demonstration of Archimedes principle.

Consider a cube of material that has side length L. If you were to push the object under water until the upper flat surface was just at the water's surface, what would the force be to hold it there?

Understanding that pressure acts perpendicular to the submerged surface, there is only one surface that provides an upward force. That is the bottom surface. The side faces only see a pressure force that tries to crush the cube so there is no vertical component. The pressure at depth L is

P = rho * L
where rho is the density of water in the units of weight per unit volume of fluid and L is the depth which is the length of the cube's edge.

The upward force is therefore

F = P * A = P * L * L

where A is the area of a cube face.

P = rho * L

so

F = rho * L * L * L

L^3 is the volume. So in this case the upward force is the density of the fluid (weight units) times the volume. Volume is the amount of fluid displaced by the submerged object.

For objects that have curved surfaces or if the cube were not oriented as here the problem becomes considerably more complicated and involves calculus to figure out. But Archimedes did the figuring for us. While what I have written does not prove anything, it nevertheless provides an easily understandable example providing you know that pressure is density(weight/unit volume) times depth.

 

[lionely]

I thank you so much, I will try to apply this to my questions. Which seem very difficult =.=