A spherical cell grows until its diameter doubles. How do surface area and volume change, and what does this mean for exchange with the environment?

Core Concept

Surface area scales with the square of length and volume with the cube, so doubling the diameter multiplies area fourfold and volume eightfold. The surface-to-volume ratio therefore drops to half its former value, leaving each unit of membrane to serve twice as much cytoplasm. Demand for nutrient import and waste export rises faster than the membrane area available to supply it, so diffusion becomes limiting. This scaling pressure explains why large or metabolically active cells favor flattened, elongated, or folded shapes that raise relative surface area.