Final answer:
The volume of a cell increases by the cube of the diameter, while the surface area increases by the square of the diameter, affecting the efficiency and functionality of the cell.
Step-by-step explanation:
When a cell expands in diameter, volume increases by the cube of the diameter, and surface area increases by the square of the diameter. This is because for spherical or cubical cells, the surface area formula is a function of the square of the radius (or diameter) and the volume formula is a function of the cube of the radius (or diameter). As a result, as a cell's size increases, its volume grows exponentially faster than its surface area. This has significant implications for cellular function because a lower surface area to volume ratio can lead to efficiency issues where the cell membrane cannot support the rate of diffusion required for the larger volume, possibly resulting in the cell dividing or dying.