Surface Area to Volume Ratio

Surface Area

Organisms exchange substances (oxygen, carbon dioxide, nutrients, waste) with their environment across a surface. This surface depends on the organism, for example:

• In single-celled organisms (e.g. an amoeba), the surface is the cell membrane
• In human lungs, the surfaces are the alveoli
• In fish, the surfaces are the gills
• In plants, the surfaces are the leaves

Volume

The amount of substance organisms need to exchange depends on their volume. If organisms have a larger volume, they have more cells, so a greater demand for nutrients. It makes sense that someone who is larger (i.e. has a higher volume) would have higher total energy requirements than someone who is smaller (i.e. lower volume).

The ratio between these two, the surface area to volume ratio (SA:V), determines whether the organisms can use simple diffusion, or whether specialised exchange surfaces and transport systems are needed. (You’ll learn what these specialised transport systems are in this unit.)

Calculating SA:V Ratio

As an organism (or structure) gets larger, its volume increases faster than its surface area, so its SA:V ratio decreases.

The image above shows three worked examples.

• Doubling the side length of a cube (1 cm → 2 cm) halves the SA:V ratio (6:1 → 3:1).
• The 2 cm cube and the 4 × 2 × 1 cuboid have the same volume (8 cm³), but the cuboid has a higher SA:V (3.5:1 vs 3:1).
  • Flatter / more elongated shapes give a higher SA:V ratio, even at the same volume.

You need to be able to calculate SA:V for any given shape (cube, cuboid, sphere). Exam questions may give the dimensions and ask you to work it out. You’ll be given the formula for a sphere, so don’t worry about memorising it.

Single-celled vs Multicellular Organisms

• Single-celled organisms have a large SA:V ratio. This means they can absorb and release gases (and other substances) by diffusion directly across their outer surface.
• Multicellular organisms have a smaller SA:V ratio. Diffusion across the body surface alone is too slow to meet the demands of all their cells (long diffusion distances, slow rate of diffusion).
• They compensate with adaptations and development of specialised systems:
  • Flattened or elongated body shapes (e.g. flatworms), which increase the surface area relative to volume
  • Folded / branched exchange surfaces. Alveoli in lungs, villi in the small intestine, root hairs in plants, all increase surface area
  • Mass transport systems. The circulatory system in animals and xylem/phloem in plants move substances quickly between exchange surfaces and tissues

SA:V and Metabolic Rate

Smaller organisms have a higher SA:V ratio, so they lose heat to the environment more rapidly (especially in cold environments).

To maintain a stable body temperature, they need a higher metabolic rate. A higher metabolic rate means more respiration, so more heat is released.

Examples include:

• Small mammals (e.g. shrews, mice) have a high SA:V so they lose heat rapidly. To compensate, they have a high metabolic rate and must eat frequently to fuel respiration.
• Large mammals (e.g. elephants, whales) have a low SA:V, so they lose heat slowly. Because of this, they don’t need as high a metabolic rate per unit mass.

Animals in cold climates often have compact body shapes (e.g. seals are rounder with shorter limbs) to reduce SA:V and minimise heat loss. The reverse is true for animals in hot climates.

Exam Question Practice