Why is a large part of an iceberg under water though ice is lighter than water?
Ice floats in water because it is lighter (less dense) than water, the medium in which it floats but with most part of the solid ice under water. This is simply because ice and water differ in their densities only in a small way. Water in liquid form at normal room temperature has a density of 1 gm/cc while in solid form as ice has a density of 0.92 gm/cc. That is, ice is lighter than water only by about 8%. Turning to explain the extent of immersion/floatation, we need to invoke the law of flotation which states that any solid floating in a liquid displaces equal weight of the liquid over which it floats.
Any solid object placed over a liquid starts sinking and displaces liquid with the volume of liquid it displaces equal to the volume of the solid it is immersed in. Depending on the densities of the solid and the liquid, the extent of immersion-sinking varies. Because, the displaced liquid generates an upward force called buoyant force eventually determining the extent of immersion which is responsible for keeping afloat solid object(s) in liquid(s).
As the solid object is put in a liquid, the solid gets sinking/immersed. This process of sinking or immersion goes on until weight of the solid equals the weight of the displaced liquid. At the point of equalizing their weights, it starts floating. So in the case of ice by virtue of its density being lighter the sinking process can go on upto 92 % its volume of the iceberg immersed in water while the remaining 8 % floating. Because 92% of water displaced will equal the weight of the solid ice floating. Hence this makes only smaller part of 8 % (tip!) of the iceberg floating while the rest get immersed in water. Interestingly when the same ice is placed in sea-water, it will float slightly more because sea water is more dense than normal/river water.