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As the volume of a cell grows, the surface area grows but not as quickly.
The surface area to volume ratio of a cell affects the rate of diffusion in that the higher the ratio, the faster the rate of diffusion. This is a directly proportional relationship.
The surface area will increase one hundred fold.
I believe it is all to do with diffusion.The solvent particles will move from an area of high concentration to the area of low concentration (the cell).
If the diameter doubles (x 2), the surface area quadruples (x 4).So if the original surface area is 3 units, the new one will be 12 units.