Surface Area to Volume Ratio and Exchange Systems

Calculating and Comparing SA:V Ratios

To compare the SA:V ratio of different sized organisms, we can model them as cubes. The surface area is the total area of the outer surface exposed to the environment, and the volume is the total internal space occupied.

Formulas for a Cube:

• Surface Area (SA): Length $\times$ Width $\times 6$
• Volume (V): Length $\times$ Width $\times$ Height

Worked Example: Calculate the SA:V ratio for a cube with a side length of $4\,cm$.

Step 1: Calculate the Surface Area.

• Area of one side = $4\,cm \times 4\,cm = 16\,cm^2$
• Total Surface Area = $16\,cm^2 \times 6 = 96\,cm^2$

Step 2: Calculate the Volume.

• Volume = $4\,cm \times 4\,cm \times 4\,cm = 64\,cm^3$

Step 3: Write as a ratio and simplify to $n:1$.

• Ratio = $96:64$
• Divide both sides by 64 $\rightarrow 1.5:1$

Comparison Table:

Side Length ($L$)	Surface Area ($6L^2$)	Volume ($L^3$)	SA:V Ratio	Simplified Ratio ($n:1$)
$1\,cm$	$6\,cm^2$	$1\,cm^3$	$6:1$	$6:1$
$2\,cm$	$24\,cm^2$	$8\,cm^3$	$24:8$	$3:1$
$3\,cm$	$54\,cm^2$	$27\,cm^3$	$54:27$	$2:1$
$4\,cm$	$96\,cm^2$	$64\,cm^3$	$96:64$	$1.5:1$
$5\,cm$	$150\,cm^2$	$125\,cm^3$	$150:125$	$1.2:1$
$10\,cm$	$600\,cm^2$	$1000\,cm^3$	$600:1000$	$0.6:1$

This table clearly demonstrates that as size increases, the SA:V ratio decreases.

Why Multicellular Organisms Need Transport Systems

Why can a single-celled amoeba survive by just absorbing oxygen directly, while a human needs a complex respiratory system? Single-celled organisms have a large SA:V ratio, meaning they can rely entirely on simple diffusion across their outer membrane to take in oxygen and remove waste. They do not have or need mass transport systems.

However, multicellular organisms have a very small SA:V ratio. Because of their size, the distance from their external surface to their innermost cells is too great. This creates a long diffusion distance, making simple diffusion far too slow to reach deep-seated cells.

Furthermore, larger animals have a high metabolic demand to support movement and maintain body temperature. Simple diffusion cannot supply oxygen and glucose, or remove carbon dioxide, fast enough to keep the organism alive. To overcome this, multicellular organisms have evolved specialised exchange surfaces and mass transport systems (like the circulatory system) to move substances over long distances quickly.

Adaptations of Exchange Surfaces

You can easily fold a massive bedsheet to fit into a small drawer; similarly, organisms fold their internal tissues to pack a massive surface area into a small space. Exchange surfaces are highly adapted to maximise the rate of diffusion. They typically feature a large surface area to allow more particles to pass through at once, and very thin membranes (often one cell thick) to provide a short diffusion path.

In animals, exchange surfaces often have an efficient blood supply to quickly move substances away from the area. This maintains a steep concentration gradient, which keeps the rate of diffusion high. Animal systems also use ventilation (breathing or water flow) to constantly refresh the external medium.

Examples of Exchange Surfaces:

• Alveoli (Lungs): Have a huge total surface area, one-cell thick walls, and an extensive capillary network.
• Villi (Small Intestine): Covered in microvilli to further increase surface area, with thin walls and a rich blood supply.
• Gills (Fish): Made of filaments and thin, plate-like lamellae to massively increase surface area, alongside constant ventilation from water flow.
• Root Hair Cells (Plants): Feature long, thin extensions to increase the surface area for absorbing water and mineral ions.
• Leaves (Plants): Their flattened shape increases surface area, while internal air spaces increase the area available for carbon dioxide absorption.