Cell size and surface area-to-volume ratio

What the exam asks

• Section I (Multiple Choice): Calculate and compare $SA:V$ ratios of spheres, cubes, cylinders, or rectangular solids; identify which cell model diffuses materials fastest; link small body mass to high mass-specific metabolic rate.
• Section II (Free Response): Frequently appears in Q1/Q2 (Experimental Results) via diffusion-rate lab data, Q4 (Conceptual Analysis) on structural adaptations, or Q5 (Analyze a Model) comparing cell shapes.
• Common task verbs: Calculate (show setup, units, and appropriate rounding), Explain (connect $SA:V$ ratio to diffusion efficiency across the plasma membrane), and Predict (how changing cell shape or losing membrane folds alters transport).

Core ideas

1. Why surface area-to-volume ratio limits cell size

• Volume ($V$) determines the amount of cytoplasm and the cell’s metabolic demand (how much nutrient intake and waste removal is needed per unit time).
• Surface area ($SA$) determines the area of plasma membrane available for material exchange (diffusion, active transport) with the environment.
• As a cell grows, its volume increases faster (cubed, $L^3$) than its surface area (squared, $L^2$). Therefore, as cell size increases, the $SA:V$ ratio decreases.
• If a cell grows too large, its plasma membrane lacks sufficient surface area to supply the large volume with nutrients (e.g., $\text{O}_2$, glucose) or expel wastes (e.g., $\text{CO}_2$, urea) quickly enough by diffusion, and diffusion distances to the center become too long.

2. Geometric formulas on the Equations and Formulas sheet

You do not need to memorize these formulas—they are provided on the AP Biology Equations and Formulas sheet—but you must apply them accurately and simplify to a unit value (e.g., $3:1$ or $3\text{ }\mu\text{m}^{-1}$).