Two spherical unicellular organisms, X and Y, have the same cytoplasmic composition, metabolic pathways, and live in identical nutrient-rich aerobic conditions. The diameters of X and Y are, respectively, 10 and 20 m . When nutrients are not limiting, the ratio of total oxygen consumption per hour per cell of organisms Y to X is:

Step-by-step solution

The total oxygen consumption per cell, when nutrients and oxygen are not limiting, is directly proportional to the volume of the cell (amount of metabolically active cytoplasm). The volume of a spherical cell is given by V = 4 3 r^3 = 1 6 d^3 . The ratio of the volume of organism Y to organism X is V_Y V_X = ( d_Y d_X )^3 . Substituting the given diameters, d_Y = 20 m and d_X = 10 m , we get V_Y V_X = ( 20 10 )^3 = 2^3 = 8 . Therefore, the ratio of total oxygen consumption per hour per cell of Y to X is 8:1 . Answe