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In a multi-stage compressor, the design typically involves stages that progressively compress the gas to achieve a higher pressure. As we move from the first stage to subsequent stages, the diameter of the cylinders usually decreases.

The reason the cylinders in the third stage are smaller than those in the first stage is primarily due to the nature of gas compression. In the initial stages, a larger cylinder is needed to handle the volume of gas being compressed at lower pressures. As the gas is compressed, its volume decreases, resulting in a lower volume that needs to be handled in the later stages. The smaller cylinders in the third stage allow for more efficient compression of an already compressed gas, optimizing energy use and maintaining the pressure ratio across the stages.

This design principle helps in managing the overall size and efficiency of the compressor, as a single large cylinder would be less efficient in handling the high-pressure gas produced by the previous stages. Hence, the smaller cylinders in the third stage fulfill the necessary requirements for efficient multi-stage compression.