Cell models

It's straightforward to model cells using cubes.

It’s straightforward to model cells using cubes.

We can investigate the effect of increasing size on surface area to volume ratios using models based on cubes:

A table showing the volume of ratios

So, as the volume increases, the surface area does not increase at the same rate.

If a graph is drawn:

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 highlighted mark?

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.

A Graph of the surface area

In the below table scientists have estimated the surface area:volume ratios of various organisms.

OrganismSurface area in square metresVolume in cube metresSurface area:volume
Bacterium6 × 10-121 × 10-186 000 000:1
Blow fly6 × 10-41 × 10-6600:1
Whale6 × 1041 × 1060.06:1

Large organisms have:

  • mechanisms to increase surface area proportionately, such as additional absorbing areas or adaptations of shape
  • transport systems and keep distances for diffusion to a minimum

Organisms living in harsh environmental conditions may reduce their surface area, eg cacti, to reduce loss of water.