How to Calculate the Relationship Between Surface Area and Volume (Biology) (2023)

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 thesurface area to volume ratioenter factor.

Surface-volume ratio, also known as sa/vol or SA:V, refers tohow much surface area an object or collection of objects has per unit volume.

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

So what is the difference between cell size, surface area, and volume? We'll see!

The surface area and volume determine thecell size. Most animal and plant cells are between 0.01 and 0.10 mm in size and cannot be seen with the naked eye (the smallest you could see is about 0.05 mm). Cell size is usually measured in micrometers (μm).

In geometry, an objectsurface areais the area occupied by the surface of the object, while itsvolumeis the amount of space inside it.

surface area and volume

In biology, bothsurface areayvolumeThey play an important role in the exchange of materials in a cell. In this case, the surface refers to thetotal areaof the organism that is exposed to the external environment. Volume refers to the total amount of space within the organism.

Surface area to volume ratio (SA:Vol)

The ratio of surface area to volume (S/V ratio)refers to the amount of surface area an object has in relation to its size. To calculate the surface area/volume ratio (S/V ratio), you candivide 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 the relationship between surface area and volume, we'll use an example of a cube.As the size of the cube increases, the volume will increase faster than the surface area, and the ratio will decrease.

Figure 1 -Surface area to volume ratio of a cube

Calculation of 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)

Important to note: area will always be in square units and volume will always be in cubic units!

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

As we've covered, as the cube's side length increases, the ratio will decrease.cells they are more of a sphere shape, but they are not perfectly spherical.

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

Figure 2 -a sphere. r: radius of a sphere

For a sphere:

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

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

Notes: π (pi) ~3.14 (3 square feet)

As the radius of a sphere increases, the surface area will increase as a function squared and the volume will be cubed. Therefore, with increasing radius, the volume will increase more quickly. At some point, with expanding size, the ratio will be too low, and substances won't be able to get in or out long enough for the cell to survive. Substances will not be distributed fast enough through diffusion within the cell.

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

What is the biological significance of size and the relationship between surface area and volume?

Organisms transfer materials between the internal and external environments to survive. prokaryotic andeukaryotic cellsrequire a smaller size. This is to facilitate efficiencysubstance exchange. Smaller unicellular organisms may depend on gas diffusion and material exchange. A higher surface area to volume ratio allows these organisms to be more efficient. Larger organisms, such asanimals, they need specialized organs to facilitate the exchange of substances.

Helungsare organs adapted togas exchangeinhumans.

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

• Passive (no power required) bydiffusion(movement of molecules)osmosis(movement ofwater molecules).
• active byActive transport(metabolic energy required).

You can find more information about the movement of energy in our articles aboutActive transport, diffusion andosmosis.

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

Increased ratio of surface area to volume

Cells and tissues that are specialized for the exchange of gases and materials will have different adaptations to facilitate efficient exchange.

We can use an example of intestinal tissue. The small intestine has adaptations to absorb 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 that increase the surface area. The folds project a finger-like tissue calledvillito further increase the surface. The villi are lined with blood capillaries to increase the amount of dissolved and digested food that can be absorbed into the bloodstream.

Fig. 3 -A simplified structure of the intestinal villus

The lungs have alveoli, which are small sacs at the end of the bronchioles. The blood and lungs exchange oxygen and carbon dioxide in the alveoli. The walls of the alveoli are very thin, and they also have membranous extensions called microvilli, which increases the total surface area of ​​the membrane.

Dangers of increasing area

We have established that a cell with a high volume would not survive as it would not facilitate the efficient movement of material within the cell and with the outside environment. The increased surface area can also cause problems. More surface area means more contact with the external environment, leading to greater water loss, heat loss, and dissolved substance loss. Furthermore, especially inextremophiles, temperature control could be affected in unfavorable conditions.

Extremophiles, organisms that live in extreme environments, have a small surface area to volume ratio. They live in difficult or impossible environments, such as the deep ocean floor, geothermal hot springs, and deserts.

For example, polar bears at the North Pole have a small surface area to volume ratio to minimize heat loss from tissue and a thick layer of blubber to keep them warm.

(1) KeyStageWiki (2021). Ratio of surface area to volume. Available at: https://keystagewiki.com/index.php/Surface_Area_to_Volume_Ratio [Accessed: 03/11/2021].