An egg contains 90% of water. When it is boiled, the water inside it cannot escape as water vapor because of the covering of calcium carbonate shell. After boiling, when the egg becomes solid the water cannot be seen. So what happens to the water inside the egg when it is boiled?
The water present in the egg is a colloidal solution of mainly proteins in water. On boiling proteins get coagulate. The coagulate proteins absorb water (solvent and it disappear).
An egg contains 90% of water. When it is boiled, the water inside it cannot escape as water vapor because of the covering of calcium carbonate shell.
That is correct, the water is still in there. Also, you are not really boiling the egg but the water bath it is in. If you place a zip lock bag filled with water into boiling water, the water in the bag will not boil and the bag will not pop open.
After boiling, when the egg becomes solid the water cannot be seen.
Yes, you would expect water at room temperature to be a liquid, but there is no visible liquid in a hard-boiled egg. This is the same when you make jello by adding a small amount of gelatin to a large amount of water (or an agarose or polyacrylamide gel). The wikipedia article on gels states:
By weight, gels are mostly liquid, yet they behave like solids due to a three-dimensional cross-linked network within the liquid.
So the answer to your question is that the water is still there but now behaves like a solid because the egg white protein that was dissolved in it changed conformation and physical properties (from a soluble globule to a sticky extended structure).