Seemingly every day we hear about the terrifying eroding of the polar ice caps at the north pole. To some it's a sign of the apocalypse, to others a heartbreaking threat to the local ecosystem. To some it's even a trade route opportunity (???). But if that much ice is melting, and global warming causing the polar ice to melt will make water level rise, then why hasn't the water level been increasing?
The ice at the north pole is floating in the water. If you drop pieces of ice into a glass of water, and note the water line, then let the ice melt, you will see that the water line doesn't increase. Floating ice that melts doesn't contribute water. (Proof is below)
So what's the problem? The ice at the south pole is on land, and there's a hell of a lot more of it. When that goes, say goodbye to our coastal cities, hello to all manner of inclement weather and worldwide famine threat.
In any case, it's a good physics problem.
Suppose a mass 
goes from solid phase to liquid. How does the water level change? The water level is the volume of liquid plus the volume of the solid that is submerged. Let
the volume of the solid
the volume of the solid that's submerged
the density of the solid phase
the density of the liquid phase
The volume occupied by before it melted was 
. 
can be found by applying Archimedes' principle: the weight of the solid is equal to the weight of water displaced
by the solid, for something floating in static equilibrium. This implies
so that the volume that determines the water level is
The volume occupied by afterward is 
. So, the change in volume that determines the water level is
Now, this proof does not work if the ice is touching the bottom of the glass, or the sides of the glass. It does, however, work for any substance that will float in solid phase (i.e. any substance that expands when solidifying).