Cell models
Cells can be modelled using cubes.
We can investigate the effect of increasing size on surface area to volume ratios using models based on cubes:
So, as the volume increases, the surface area does not increase at the same rate.
If a graph is drawn:
Question
What is the surface area to volume ratio of the cube with a length of 6?
This cube will have a surface area : volume ratio of 1.
The volume = 6 × 6 × 6 = 216
The surface area = 6 × (6 × 6) = 216
A stacked bar chart can be drawn to illustrate the proportions of surface area and volume.
In the below table scientists have estimated the surface area : volume ratios of various organisms.
| Organism | Surface area (m2) | Volume (m3) | Surface area : volume |
| Bacterium | 6 x 10-12 | 1 x 10-18 | 6 000 000 : 1 |
| Blow fly | 6 x 10-4 | 1 x 10-6 | 600 : 1 |
| Whale | 6 x 104 | 1 x 106 | 0.06 : 1 |
| Organism | Bacterium |
|---|---|
| Surface area (m2) | 6 x 10-12 |
| Volume (m3) | 1 x 10-18 |
| Surface area : volume | 6 000 000 : 1 |
| Organism | Blow fly |
|---|---|
| Surface area (m2) | 6 x 10-4 |
| Volume (m3) | 1 x 10-6 |
| Surface area : volume | 600 : 1 |
| Organism | Whale |
|---|---|
| Surface area (m2) | 6 x 104 |
| Volume (m3) | 1 x 106 |
| Surface area : volume | 0.06 : 1 |
Large organisms:
- have mechanisms to increase surface area proportionately, such as additional absorbing areas or adaptations of shape
- have transport systems and keep distances to a minumum for diffusion
Organisms living in harsh environmental conditions may reduce their surface area, eg cacti, to reduce loss of water.
