Let's start by defining "dense" in scientific terminology.
"Density" means "the mass of a unit volume of some material." In the case of your
problem, the unit volume we're discussing is the amount of H2O contained in the small
lake. In a liquid form, H2O is called water. In a solid form, H2O is called
ice.
In your problem, you are imagining that ice (the solid
form) is more dense than water (the liquid form). As the more dense substance, the ice
would have a higher specific gravity. If the top one inch of water in the lake froze and
became ice, that top one inch of ice would become more dense than the water below it.
Because of that greater density, the ice would sink down into the less dense, still
liquid water below it.
In reality, the solid form of H2O is
less dense than the liquid form. That's why ice floats on top of the lake as lake water
freezes.
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