AP Biology · Unit 2 · Topic 2.2
Every cell trades with its surroundings across its surface, but its needs grow with its volume. That race is what sets how big a cell can get.
Learning objective 2.2.A Explain the effect of surface area-to-volume ratios on the exchange of materials between cells or organisms and the environment.
Narrated walkthrough of the “Grow a cell” tab. Captions are on by default.
A cell takes everything in across its surface, but everything inside needs supplying. Grow the cell and watch the two quantities pull apart — the shaded rim is the part a substance can reach from outside, and the pale core is what it cannot.
A sphere of diameter s and a cube of side s happen to have exactly the same ratio, because 3/r and 6/s are the same number. So comparing shapes by size tells you nothing. Hold the volume fixed instead, and the differences appear.
Surface area-to-volume ratio against size, for the shape and folding you have chosen. The marked point is where your slider is. When the membrane is folded, the dashed line is the same shape unfolded.
Surface area grows with the square of length. Volume grows with the cube. Double a cell and its surface area goes up four times while its volume goes up eight, so the ratio halves. Every time.
For a cube of side s the ratio is exactly 6/s. For a sphere of radius r it is exactly 3/r. Both are just the formula, simplified — and both shrink as the cell gets bigger.
A falling ratio affects a cell's ability to . All four are exchanges across the surface, and all four get harder as the inside grows faster than the outside.
This is why surface area-to-volume ratio can restrict cell size and shape. Smaller cells typically have a higher ratio and exchange materials more efficiently than larger ones.
A cell that needs to be big can raise its surface area without changing its volume, by folding its membrane. Push the folding slider up and watch the ratio climb back while the volume stays put.
The same trick appears inside the cell: a mitochondrion's inner membrane is highly convoluted for exactly this reason, and root hairs, gut epithelial cells and cilia all use folds or projections to raise exchange area.
As organisms get bigger, their surface area-to-volume ratio falls too, which changes the rate of heat exchange with the environment. A smaller mass exchanges proportionally more heat than a larger one.
Ratios in cm² per cm³, written cm⁻¹, with each animal treated as a sphere of density 1 g/cm³.
There is also a relationship between metabolic rate per unit body mass and size: typically, the smaller the organism, the higher the metabolic rate per unit of body mass.
Each card gives you a situation. Choose what the surface area-to-volume argument predicts.
Answer these in your own words before you open the answers.
1. SA = 6s² = 6 × 16 = 96 square units. V = s³ = 64 cubic units. SA:V = 96/64 = 1.5. This also matches the shortcut 6/s = 6/4 = 1.5.
2. Surface area grows with the square of length while volume grows with the cube. Volume therefore increases faster than surface area, so dividing one by the other gives a smaller number as the cell gets bigger.
3. Fold the membrane, or develop projections. Folding increases the surface area available for exchange without increasing the volume, so the SA:V ratio rises again and the larger cell can still exchange enough with its surroundings.
4. The mouse. It is smaller, so it has a higher surface area-to-volume ratio, and a smaller mass exchanges proportionally more heat with the environment than a larger mass. The mouse also has a higher metabolic rate per unit body mass.