Surface Area to Volume Ratio

All living organisms are made up of cells. Some, like humans, have numerous cells while others only have one. With a few exceptions, individual cells are tiny and can only be seen through a microscope. Why are cells so small? This is where the surface area to volume ratio factor comes in.

What is the difference between the cell size, surface and volume?

So, what is the difference between cell size, surface area, and volume? Let's take a look!

The surface area and volume determine the cell size. Most animal and plant cells are between 0.01 and 0.10 mm in size and cannot be seen by the naked eye (the smallest you would be able to see is about 0.05 mm). Cell size is usually measured in micrometre (μm).

Surface Area and Volume

In biology, both surface area and volume play an important role in a cell's exchange of materials. In this case, the surface area refers to the total area of the organism that is exposed to the external environment. The volume is refers to total amount of space inside the organism.

Surface area to volume ratio (SA:Vol)

The surface area to volume ratio (S/V ratio) refers to the amount of surface an object has relative to its size. To calculate the surface are to volume ratio (S/V ratio), you can divide the surface area by the volume.

• The lower the ratio, the slower the transport of the molecules within the cell and with the surrounding environment.

To help you understand surface to volume ratio, we will use an example of a cube. As the size of the cube increases, the volume will increase more rapidly than the surface area, and the ratio will decrease.

Fig. 1 - Surface to volume ratio of a cube

Calculating the ratio of a cube (Figure 1):

SA = area of one side x 6 sides (example: 1 cm x 1 cm x 6 cm) = 6 cm2)

Vol = length x width x height (example: 1 cm x 1 cm x 1 cm = 1 cm2)

$$ \textbf{S/V ratio} = \frac{\textbf{Surface Area}}{\textbf{Volume}} $$

As we have covered, as the length of the side of the cube increases, the ratio will decrease. Cells are more of a sphere shape, but they aren't perfectly spherical.

Imagine a cell being a sphere. Here is an example.

For a sphere:

$$ \textbf{Surface Area = 4}\times \Pi\times r^{3} $$

$$ \textbf{Volume = }\frac{4}{4}\times \Pi\times r^{2} $$

As the radius of a sphere increases, the surface area will increase as a squared function, and volume will be cubed. Thus, with the increasing radius, the volume will increase more rapidly. At some point, with the expanding size, the ratio will be too low, and the substances will not be able to enter or leave in a sufficient time for the cell to survive. Substances will not be distributed fast enough via diffusion within the cell.

The cell will stop growing when there is just enough surface area to efficiently distribute the substances within the cell and the surrounding environment.

What is the biological importance of size and surface area to volume ratio?

Organisms transfer materials between the inner and the outer environments to survive. Prokaryotic and eukaryotic cells require a smaller size. This is to facilitate efficient substance exchange. Smaller single-celled organisms can rely on diffusion for gasses and material exchange. A higher surface area to volume ratio allows these organisms to be more efficient. Larger organisms, such as animals, need specialised organs to facilitate substance exchange.

Except for the heat, the exchange will happen in two ways:

• Passive (no energy required) by diffusion (movement of molecules) or osmosis (movement of water molecules).
• Active by active transport (metabolic energy required).

The size and metabolic rate of the organism will affect the amount of material exchanged. Organisms with higher metabolic rates will need to exchange a larger amount of substances and, in turn, will require a higher SA:Vol ratio.

Increasing surface area to volume ratio

Cells and tissues that are specialised for gas and material exchange will have different adaptations to facilitate an efficient exchange.

We can use an example of the intestinal tissue. The small intestine has adaptations for absorbing nutrients and minerals from food. The inner wall of the small intestine, mucosa, is lined with simple columnar epithelial tissue. The mucosa is covered in folds that are permanent features of the wall increasing the surface area. The folds project finger-like tissue called villi to increase the surface area further. Villi are filled with blood capillaries to increase the amount of dissolved, digested food that can be absorbed into the bloodstream.

Fig. 3 - A simplified structure of the intestinal villus

Dangers of increased surface area

We have established that a cell with a high volume would not survive as it would not facilitate efficient material movement within the cell and with the outside environment. The increased surface can cause problems too. More surface area means more contact with the external environment, leading to more water loss, heat loss and loss of dissolved substances. In addition, especially in extremophiles, temperature control could become impaired in unfavourable conditions.