Explain how the surface area to volume ratio limits cell size and exchange.

What this dot point is asking

The geometry of size

Every cell exchanges materials, oxygen, nutrients, carbon dioxide, and waste, across its surface, the membrane. The need for these materials depends on the volume of living cytoplasm inside. The problem is that surface area and volume do not grow at the same rate.

Consider a cube. If its side doubles, the surface area (sides squared) increases by four times, but the volume (sides cubed) increases by eight times. So as the cube grows, volume outpaces surface area and the surface area to volume ratio falls.

Why a high ratio matters

A high surface area to volume ratio is good for a cell because:

• The large surface allows enough oxygen and nutrients to enter, and enough waste to leave, for the whole volume.
• The short distance from the surface to the centre means diffusion can supply the middle of the cell quickly.

As a cell enlarges and its ratio falls, the surface can no longer supply the interior fast enough, and diffusion distances become too long. The cell's needs outstrip its ability to exchange materials.

Solutions to the size problem

Organisms get around the limits of the ratio in several ways:

• Staying small and dividing: most cells divide once they reach a limiting size, keeping each cell's ratio high. This is why large organisms are built from huge numbers of small cells, not a few giant ones.
• Changing shape: a flat or elongated cell has a higher ratio than a sphere of the same volume. Cells specialised for absorption, such as those lining the small intestine, are often thin and folded.
• Folding the surface: structures such as microvilli on intestinal cells, the folded inner membrane of mitochondria, and root hair extensions all increase surface area without greatly increasing volume.

Scaling up to whole organisms

The same principle applies to entire organisms. A single-celled organism can exchange gases across its whole surface, but a large multicellular animal cannot rely on its outer surface alone, because its surface area to volume ratio is too low. Large organisms therefore evolve specialised exchange surfaces with very large areas, such as lungs, gills, and the network of capillaries, and transport systems to carry materials to and from every cell. These adaptations are explored in the gas exchange and transport notes.

Heat and the ratio

Surface area to volume ratio also affects heat exchange. Small animals lose heat quickly because they have a large surface relative to their volume, which is why small warm-blooded animals must eat often to replace lost heat. Large animals retain heat more easily. The same geometry that controls material exchange also shapes how organisms manage temperature.