#57 Cell size

Cell size is limited because of a surface area-to volume ratio. As the cell grows, the surface area will not increase as fast as the volume will. Cells need to transport nutrients if the cell becomes to big then the volume would increase faster than the surface area and nutrients would not be able to exit and enter the cell quickly enough. The diagram above shows how surface area cannot increase as fast as volume.
In the first figure, it shows how all cubes have volume as well as surface area and the surface area is equal to all the areas of the six sides of the cube combined. Remember that the formula for area is length X width.
In figure two, the first cube is split into eight small cubes giving it 48 sides. The volume is still the same but the surface area has now doubled.
In figure three, each of the eight cubes has been split into eight smaller cubes and we now have 64 cubes when together still have the same volume of the first cube but the surface area has doubled.
Source: Pg 73