Question

As a cell grows, volume increases faster than surface area, what happens to the SA:Vol ratio?

A. SA increases faster than V, resulting in an increasing SA:V ratio.

B. SA and V increase at the same rate, maintaining a constant SA:V ratio.

C. V increases faster than SA, resulting in a decreasing SA:V ratio.

D. SA and V are inversely proportional, resulting in a fluctuating SA:V ratio.

Answer 1

The surface area-to-volume ratio decreases as a cell grows because volume increases faster than surface area.

Step-by-step explanation:

As a cell grows, its volume increases faster than its surface area, leading to a change in the surface area-to-volume ratio. The correct answer to what happens to the SA:Vol ratio is: C. Volume increases faster than surface area, resulting in a decreasing SA:V ratio.

In mathematical terms, the surface area of a cell increases as the square of its radius (for example, 4πr²), but the volume increases as the cube of its radius (for example, ⅓ × 4πr³). This disparity in the rate of increase means that as the cell grows and becomes larger, the ratio of surface area to volume decreases. This phenomenon has significant implications for the efficiency of a cell's metabolism and transport of substances across the cell membrane, often limiting the maximum size a cell can reach before it must divide or risk dying.