# Surface Area to Volume Ratio

## Understandings: Surface area to volume ratio is important in the limitation of cell size.

Many reactions occur within the cell. Substances need to be taken into the cell to fuel these reactions and the wast products of the reactions need to be removed. When the cell increases in size so does its chemical activity. This means that more substances need to be taken in and more need to be removed. The surface area of the cell is vital for this. Surface area affects the rate at which particles can enter and exit the cell (the amount of substances that it takes up from the environment and excretes into the environment), whereas the volume affects the rate at which material are made or used within the cell, hence the chemical activity per unit of time.

As the volume of the cell increases so does the surface area however not to the same extent. When the cell gets bigger its surface area to volume ratio gets smaller. To illustrate this we can use three different cubes. The first cube has a side of 1 cm, the second 3 cm and the third 4 cm. If we calculate the surface area to volume ratio we get:

Cube 1
Surface area: 6 sides x 12 = 6 cm2
Volume: 13 = 1 cm3
Ratio = 6:1

Cube 2
Surface area: 6 sides x 32 = 54 cm2
Volume: 33 = 27 cm3
Ratio = 2:1

Cube 3
Surface area: 6 sides x 42 = 96 cm2
Volume : 43 = 64 cm3
Ratio = 1.5:1

As we can see the cube with the largest surface area and volume has the smallest surface area to volume ratio. If the surface area to volume ratio gets too small then substances wonâ€™t be able to enter the cell fast enough to fuel the reactions and wast products will start to accumulate within the cell as they will be produced faster than they can be excreted. In addition, cells will not be able to lose heat fast enough and so may overheat. Therefor the surface area to volume ratio is very important for a cell.

Summary:

- Substances need to be taken in to the cell to fuel reactions & waste products need to be removed
- Increase in cell size leads to increase in chemical reactions --> more substances needed in and more substances needing to be removed
- Surface area affects the rate at which particles enter and exit the cell
- Volume affects the rate of the chemical activities
- When the volume increases so does the surface area but not to the same extent
- As the cell gets larger, its surface area to volume ratio gets smaller
- If the ratio gets too small, particles will not be able to enter and exit the cell fast enough
- Results in accumulation of waste products and overheating of the cell