Cell Size and Surface Area to Volume: As the size of a cell decreases, how does its surface area to volume (SA:V) ratio change?

Introduction / Context:
Transport, heat exchange, and reaction rates in cells depend on geometry. The SA:V ratio is a key constraint on cell size and shape.

Given Data / Assumptions:

• We are comparing geometrically similar cells shrinking uniformly.
• Surface area scales with length^2; volume scales with length^3.

Concept / Approach:
For similar shapes, SA ∝ L^2 and V ∝ L^3; therefore SA:V ∝ 1/L. As L decreases, SA:V increases, improving exchange efficiency (nutrient uptake, waste removal).

Step-by-Step Solution:
1) Let linear dimension be L.2) SA:V ∝ L^2 / L^3 = 1 / L.3) Decreasing L raises 1/L; hence SA:V increases.

Verification / Alternative check:
Microvilli increase effective surface without much changing volume—same principle.

Why Other Options Are Wrong:
Decreases contradicts scaling laws; stays the same would require area and volume scaling identically, which they do not.

Common Pitfalls:
Confusing absolute surface area with the ratio; small cells have less absolute area but higher SA:V.

Final Answer:
increases