As a cell grows, Volume ($r^3$) increases much faster than Surface Area ($r^2$)
A lower SA:V ratio severely limits the rate of diffusion/exchange
Cells adapt via folds (microvilli) or dividing to increase SA:V
Tags
SA:V RatioDiffusionCell SizeMath
6.00
Surface Area (SA)
1.00
Volume (V)
6.00
Ratio (SA/V)
Fast
Diffusion Efficiency
Cell Shape
Size Dimension ($r$ or $s$) 1.0 µm
Diffusion Simulation
Watch oxygen particles diffuse into the center of the cell. Notice how long it takes for a large cell to get oxygen to its core compared to a small cell.
Key Insight
When the SA:V ratio drops below ~1.0, the cell cannot absorb nutrients or expel waste fast enough to survive, forcing it to divide or die.