How are shape and volume used to classify solids, liquids, and gases?

Solids have a fixed shape and occupy a fixed volume.

Liquids, because they flow, can occupy whatever shape their container has, so they do not have a fixed shape. Because the particles in liquids are very close together (barely further apart than in solids) liquids do not easily compress, so their volume is fixed.

Gases can also flow, so occupy the shape of their whole container. They do not have a fixed shape. Because the particles in gases are much further apart than in liquids or solids, they can be squeezed closer together. Gases therefore can be compressed or expanded. They do not have a fixed volume.