Theoretical considerations suggest that the mammalian metabolic rate is linearly proportional to the surface areas of mitochondria, capillary, and alveolar membranes. However, the scaling exponents of these surface areas to the mammals' body mass (approximately 0.9-1) are higher than exponents of the resting metabolic rate (RMR) to body mass (approximately 0.75), although similar to the one of exercise metabolic rate (EMR); the underlying physiological cause of this mismatch remains unclear. The analysis presented here shows that discrepancies between the scaling exponents of RMR and the relevant surface areas may originate from, at least for the system of alveolar membranes in mammalian lungs, the facts that (i) not all of the surface area is involved in the gas exchange and (ii) that larger mammals host a smaller effective surface area that participates in the material exchange rate. A result of these facts is that lung surface areas unused at rest are activated under heavy breathing conditions (e.g., exercise), wherein larger mammals support larger activated surface areas that provide a higher capability to increase the gas-exchange rate, allowing for mammals to meet, for example, the high energetic demands of foraging and predation.