SOLUTION: Four cubes of ice with an edge of 4 centimeters each are left to melt in a cylindrical glass with a radius of 6 cm. how high will the water rise when they have melted?

Question 1209182: Four cubes of ice with an edge of 4 centimeters each are left to melt in a cylindrical glass with a radius of 6 cm. how high will the water rise when they have melted?
Found 2 solutions by math_tutor2020, ikleyn:
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

Each cube has a side length of s = 4 cm.
Each cube has volume s^3 = 4^3 = 64 cubic cm.
Four such identical cubes have a total volume 4*64 = 256 cubic cm.
This is also the volume of water after the ice is melted.

The water in the cylindrical glass will form a smaller cylinder of its own.
This smaller cylinder has unknown height h and radius r = 6.
V = volume of cylinder
V = pi*r^2*h
256 = pi*6^2*h
256 = 36pi*h
h = 256/(36pi)
h = 2.263537

The height of the water is around 2.263537 cm. The answer will vary slightly depending how you round it. Also, it depends how many decimal places you use in pi = 3.14...
I used the calculator's stored version of pi to get the most accuracy possible.

Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

Interesting fact from Science is that the volume of ice before melting
is GREATER than the volume of the water after melting.

It is why the ice always floats on the surface of the water
and does not sink in water.

Usually, school students learn this fact when they are 6th or 7th grade.

The difference in volumes is not so small. The ratio of the ice density
to the water density at normal conditions is about 0.92;
so the difference of volumes is about 8.7%.

Again, although the chemical formula of water in fluid state and in solid state
is the same H2O, their phase states are different.

There is no any logical or physical reason to assume that their volumes
before melting and after melting are the same.

We make this assumption with the only reason to solve the problem,
but physically and logically we have no solid base for making this assumption.

                    Physically, this assumption is wrong.

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        Physically, at the phase change, the mass conserves,
              but the volume does not necessary conserve.

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