At cellular level the function of gaseous exchange is performed by the mitochondrion of the cell.
Mitochondria is the double membranous cell organelle that performs the cellular respiration. The inner membrane is folded into finger-like structures called cristae. This increases the surface area of the organelle in order to increase the process of cellular respiration into many folds.
Cell is the basic building block of all the organisms. It consists of an outer plasma membrane and various cell organelles. These altogether perform all the functions that are necessary for the cell to be functioning and alive. The examples of cell organelles are: mitochondria, chloroplast, nucleus, etc.
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