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# 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.

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

## 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).

In geometry, an object's surface area is the area occupied by the object's surface, while its volume is the amount of space within it.

### 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)

Important to note - the area will always be in squared units, and the volume will always be in cubed units!

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

To calculate SA/vol ratio: divide the surface area by the volume. For example, in the case of an organism with a surface area of 4 meters squared (m2) and a volume of 2 meters cubed (m3), the SA:Vol ratio is 2.

$$\text{SA/vol ratio} = \frac{\text{Surface Area}}{\text{Volume}} = \frac{\text{4 m}^{2}}{\text{2 m}^{3}} = \text{2 }$$

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.

Fig. 2 - A sphere. r: radius of a sphere

For a sphere:

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

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

Note: π (pi) ~3.14 (3 s.f.)

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.

The lungs are organs adapted to gas exchange in humans.

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

More about energy movement can be found in our articles on active transport, diffusion and osmosis.

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

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

### 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.

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 bed, geothermal hot springs and deserts.

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

## Surface Area to Volume Ratio - Key takeaways

• Surface-area-to-volume ratio, also known as sa/vol or SA:V, refers to how much surface area an object or collection of objects has per unit volume.
• Cell size, surface area and volume are essential factors of substance exchange. The surface area and volume determine the cell size.
• The ratio between the surface area and volume will determine the speed of material exchange, calculated by dividing the surface area by the volume.
• The surface area and volume will not increase proportionally as the object increases in size.
• Living organisms have a number of adaptations to increase the surface area. For example, alveoli in the lungs have microvilli - membranous extensions to increase the gas exchange area.
• More surface area leads to more contact with the environment. Increased contact of a cell or an organ with the environment will increase water loss, heat loss and loss of dissolved substances.

(1) KeyStageWiki (2021). Surface Area to Volume Ratio. Available at: https://keystagewiki.com/index.php/Surface_Area_to_Volume_Ratio [Accessed: 03/11/2021].

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How to calculate surface area to volume ratio?

First determine the surface area and the volume of the shape. You will then divide the surface area by the volume to find the ratio.

What is the surface area to volume ratio?

The amount of surface area per unit volume of an object.

Why is the surface area to volume ratio important?

Organisms transfer materials between the environments in order to survive. High ratio between the surface area and volume will allow efficient substance exchange. However, if this ratio is too low, the cell will die as it will be unable to exchange enough substances to survive.

How does the surface area to volume ratio affect heat loss?

More surface area leads to more contact with the environment. Increased contact of a cell or an organ with the environment will increase heat loss.

How to find the volume of a cube with the surface area?

We can rearrange the equation for the surface area of a cube. SA = side of a cube x side of a cube x 6 sides. Since we know the length of the side of the cube, we can use that to calculate volume: Volume = length x width x height (of a side of a cube).

How to work out the surface area to volume ratio.

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 S/V ratio, you can divide the surface area by the volume

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