Surface area to volume ratio
Why cells stay small
- A cell takes in food and oxygen, and removes waste, across its surface.
- But as something grows, its volume grows faster than its surface area.
- So big cells struggle to supply their inside fast enough.
The ratio falls as size grows
For a cube of side $L$:
$$\text{surface area} = 6L^2, \qquad \text{volume} = L^3, \qquad \text{ratio} = \frac{6}{L}$$
- A bigger $L$ gives a smaller ratio.
Practice
As a cell gets larger, its surface area to volume ratio:
Volume (L³) grows faster than surface area (6L²), so the ratio 6/L falls as L increases.
Practice
A cube has side length 2. Using ratio = 6/L, what is its surface-area-to-volume ratio?
ratio = 6 / L = 6 / 2 = 3 (i.e. 3 : 1).
Why it matters
- A large surface area to volume ratio = fast exchange. So small cells and thin, flat shapes exchange materials quickly.
- Large cells cannot rely on diffusion alone — they need transport systems.
- You can show this with agar blocks of different sizes soaked in dye: the smallest block (largest ratio) changes colour all the way through fastest. (Diffusion through non-living material is studied with dialysis tubing.)
Practice
Why do small cells and thin, flat shapes exchange materials quickly?
A large ratio means lots of surface for each unit of volume, so exchange by diffusion is fast.
Practice
In the agar-block experiment, which block changes colour all the way through fastest?
The smallest block has the largest ratio, so dye/acid diffuses to its centre fastest.
You've got it
Key idea
- volume grows faster than surface area → bigger means a smaller ratio
- cube: $\text{SA}=6L^2$, $V=L^3$, ratio $=\dfrac{6}{L}$
- large ratio = fast exchange → small cells and thin, flat shapes win
- agar-block demo: the smallest block colours through fastest