Describe why a larger prokaryotic cell surface is less efficient at metabolsim (Demonstrate this mathematically!)
Because a cell’s growth rate depends, among other things, on the rate of nutrient exchange, the higher S/V ratio of smaller cells supports a faster rate of nutrient exchange per unit of cell volume compared with that of larger cells. The volume of each cell is a function of the cube of it's radius (V= 4/3
r3), while its surface area is a function of the 32 square of the radius (S = 4
r2). Therefore, the S/V ratio of a spherical coccus is 3/r. Thus, as a cell increases in size, its S/V ratio decreases.