Final answer:
The surface area does not increase as fast as the volume of a cell when it grows, leading to a decreased surface area-to-volume ratio. This can cause inefficiencies in metabolic processes due to the insufficient surface area, and may result in cell division or cell death if the cell becomes too large. The correct answer is option d) The surface area does not increase as fast as the volume does.
Step-by-step explanation:
How the size of a cell's surface area changes compared to its volume when the cell grows is a critical concept in understanding cell biology and the physical limitations that influence cell functions. When a cell's size increases, its volume grows faster than its surface area. This is because, while the surface area of a cell increases as the square of its radius, the volume increases as the cube of its radius. As a result, the surface area-to-volume ratio decreases as the cell becomes larger.
For example, if we consider a cell with a volume of 1 mm³ and a surface area of 6 mm², it has a surface area-to-volume ratio of 6 to 1. When the cell grows and the volume increases to 8 mm³ with a surface area of 24 mm², the ratio drops to 3 to 1, demonstrating that the surface area does not increase as rapidly as the volume. Therefore, the correct answer to the question is: d) The surface area does not increase as fast as the volume does. If a cell becomes too large, it can lead to inefficiencies, as the plasma membrane may not provide enough surface area to meet the increased volume's metabolic demands, leading to cell division or death.