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By definition.

There are 4 basic states of matter: solid, liquid, gas, and plasma.

That type which has no definite volume or shape is defined, in physical science, as a gas.

Solids have a definite shape and are (practically) not compressible, so their volume is also well defined. Liquids are not compressible, but they can take any shape, liquid meaning fluid (able to flow.)

Gasses are fluids which can easily be compressed, so they have no definite volume or shape. Their volume depends upon the pressure applied. Gasses are not particles. Balloons may take any shape and are always filled with some gas.

Plasma is a special case of a gas, so hot and excited that its electrons cannot stay bound to its atomic nucleus.

That state of matter which has no definite shape or volume is called a gas.

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