The Alveoli
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The surface area of the alveoli is where oxygen and carbon dioxide are exchanged across membranes. A large surface area enables a greater amount of gas transfer. The skin has two main functions: one is holding all our bits in one place and the other is to maintain body temerature. In the latter role, a large surface area is good for cooling the body but bad for keeping warm. So it is a compromise.
Leaves are broad, thin and flat to provide a large surface area, to absorb sunlight for photosynthesis. :)
Surface Area
Area
A cell's volume is the amount of material that can fit into the cell. A cell's surface area is the total amount of material that makes up the outside of the cell. The ratio of surface area to volume is the amount of surface area per unit volume of an object or collection of objects.