Density is the amount of matter in a certain volume. The more matter within a certain volume, the denser the substance or object and the greater its mass. Some objects are denser than others: their atoms are more tightly packed together than others, or they are more massive, or both. Metals such as iron are dense materials. But if the metal is made into a boat’s hull, its shape contains lots of air, which has a very low density. The overall density of the iron-plus-air is less than the density of water, and so a boat will float.

Hot-air balloon

A hot-air balloon contains matter in a gaseous state: air. Heat from the burner causes the air molecules to move apart. When there are fewer air molecules inside the balloon than in the cooler air outside it, the balloon is less dense, and so it rises into the sky.

Eureka!

The Greek scientist Archimedes was given the task of determining whether a goldsmith was stealing gold during the making of a golden wreath, replacing it with a cheap—and less dense—alloy. Archimedes took a bath and realized from the rise of the water when he got in that he could calculate the volume of the gold wreath by immersing it in a bath and measuring the amount of water it displaced. Now he could compare its volume with its mass and prove whether or not it was made entirely of gold. Archimedes leapt from his bath and went running naked through the streets shouting "Eureka!" ("I have found it!").