Bacteria and other cells show a puzzling behavior. At high growth rates, E. coli switch from respiration (which is ATP-efficient) to using fermentation for additional ATP (which is inefficient). This overflow metabolism results in a several-fold decrease in ATP produced per glucose molecule provided as food. By integrating diverse types of experimental data into a simple biophysical model, we give evidence that this onset is the result of the membrane real estate hypothesis: Fast growth drives cells to be bigger, reducing their surface-to-volume ratios. This decreases the membrane area available for respiratory proteins despite growing demand, causing increased crowding. Only when respiratory proteins reach their crowding limit does the cell activate fermentation, since fermentation allows faster ATP production per unit membrane area. Surface limitation thus creates a Pareto trade-off between membrane efficiency and ATP yield that links metabolic choice to the size and shape of a bacterial cell. By exploring the predictions that emerge from this trade-off, we show how consideration of molecular structures, energetics, rates, and equilibria can provide important insight into cellular behavior.