3.2 - Surface Area to Volume Ratio

Surface area to volume ratio

• The surface area to volume ratio (written SA : V) compares the size of an object's outer surface with the amount of space inside it.
• A ratio shows how big one value is compared with another - so a ratio of 6 : 1 means there are six units of surface area for every one unit of volume.
• It can be written three ways: as a ratio (e.g. 6 : 1), as a fraction, or as a single number (surface area ÷ volume, e.g. 6).

Why bigger organisms have a smaller ratio

• As an object gets bigger, its surface area and its volume don't grow at the same rate:
  • Surface area depends on the sides multiplied two at a time (length × width)
  • Volume depends on all three dimensions multiplied together (length × width × height)
• Volume grows faster than surface area, so a large object has a smaller surface area compared with its volume than a small object does.
• In short: the bigger an organism is, the smaller its surface area to volume ratio.

Why the ratio matters in biology

• Substances enter and leave an organism across its surface, by diffusion, while the whole volume has to be supplied.
• The surface is where exchange happens; the volume is what needs supplying.
• As an organism gets bigger, the distance a substance must diffuse from the surface to reach the middle also grows.
• A large surface area compared with the volume, and a short diffusion distance, both make exchange easy.

Worked example - Surface area to volume ratios

An elephant is modelled as a block 8 cm by 8 cm by 4 cm, and a shrew as a 2 cm cube. Work out the surface area to volume ratio of each, giving both in the form n : 1, and say which is larger.