The surface area of a cell is approximated by the surface area of a sphere, given by the expression, 4πr². The volume of the spherical cell is given by the expression, 4πr³/3. The ratio between surface area and volume turn out to be, 1:r/3, or 3:r. This indicates that the SA/volume ratio is inversely related to the radius of the cell. Greater the radius, lower the ratio. Higher ratios are present in the prokaryotic cells This enables them to exchange food and water from their environment by the simple process of osmosis and diffusion. Eukaryotes have a larger cell radius and size. Thus, eukaryotes find it harder to exchange food and water by simple diffusion, rather they have specialised organelle present in the cell that actively transport food and water into the cell. These specialised organelles help the cell avoid the problem due to small SA/volume ratio.
