How does the surface area to volume ratio help single celled organisms to get 02 through diffusion?
Modeling a cell as a sphere, the volume is 4/3 pi r^3 and the surface area is 4 pi r^2; therefore the ratio is 1/3 r. So a small cell has a better ratio than a larger one. The O2 need is proportional to the volume and the diffusion rate to the surface area, hence the supply efficiency is affected by the SA:V. Think of it this way its like having more turn gates for the underground so people can get through quicker.
