Cell Size & SA:V Ratio Activity
Goal: Calculate the surface area, volume and surface-area-to-volume ratio of model cells, and explain why most cells stay small.
What to do
- Choose Cube-shaped cell and set Side length s to 1. Record the surface area, volume and SA : V ratio.
- Repeat with side lengths of 2 µm and 4 µm.
- Choose Spherical cell and press “Bacterium (1 µm across)”, “Animal cell (20 µm across)” and “Frog egg (1,000 µm across)” in turn. Record each result.
- For the challenge, press “Plant cell (50 µm across)” to check your answer.
Record your results
| Cell | Surface area | Volume | SA : V ratio |
|---|---|---|---|
| Cube, s = 1 µm | |||
| Cube, s = 2 µm | |||
| Cube, s = 4 µm | |||
| Bacterium (sphere, r = 0.5 µm) | |||
| Animal cell (sphere, r = 10 µm) | |||
| Frog egg (sphere, r = 500 µm) |
Questions
What happened to the SA : V ratio each time you doubled the side of the cube? Use SA : V = 6 / s to explain.
Calculate the surface area, volume and SA : V ratio of a spherical cell with a radius of 10 µm. Show your working.
The bacterium has an SA : V ratio of 6 per µm and the frog egg 0.006 per µm. How many times larger is the bacterium’s ratio, and what does that mean for supplying each cell by diffusion?
Predict what happens to a cell’s SA : V ratio if it doubles in diameter, then check with the SA : V if twice as large readout.
Give two ways that real cells increase their surface area without becoming smaller, with an example of each.
Challenge: a cube-shaped cell has an SA : V ratio of 0.12 per µm. How long is its side?
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