# 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.

OrganismSurface area (m2)Volume (m3)Surface area : volume
Bacterium6 x 10-121 x 10-186 000 000 : 1
Blow fly6 x 10-41 x 10-6600 : 1
Whale6 x 1041 x 1060.06 : 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.