Measuring circular areas
- Bacterial colonies and zones of inhibition are often approximately circular, so their cross-sectional area is calculated from the radius.
- Measure the diameter through the centre of the circle. If the edge is uneven, measure two perpendicular diameters and calculate their mean.
- Calculate the radius using r=d2r=\frac{d}{2}r=2d, then use A=πr2A=\pi r^2A=πr2.
Example
****A clear zone has a mean diameter of 16 mm16\,\mathrm{mm}16mm. Its radius is r=162=8 mmr=\frac{16}{2}=8\,\mathrm{mm}r=216=8mm. Therefore A=π×82=201.1 mm2A=\pi\times 8^2=201.1\,\mathrm{mm}^2A=π×82=201.1mm2, which is 201 mm2201\,\mathrm{mm}^2201mm2 to three significant figures.
Comparing antimicrobial effects
- When the same microorganism and experimental conditions are used, a larger zone of inhibition provides evidence that the antimicrobial substance was more effective.
- Area is proportional to the square of the radius. A zone with twice the radius has four times the area, not twice the area.
- Use the same units throughout. If the radius is measured in millimetres, the area must be recorded in mm2\mathrm{mm}^2mm2.
Exam technique
Show every stage: write r=d2r=\frac{d}{2}r=2d, substitute into A=πr2A=\pi r^2A=πr2, keep extra calculator digits during the calculation, and round only the final answer with the correct squared unit.
Evaluating measurements
- An irregular zone is a source of measurement uncertainty. Taking two diameters at right angles and using their mean gives a more representative radius.
- A larger clear area does not by itself prove that a medicine will work better inside a person. Diffusion through agar, concentration and experimental conditions also affect zone size.
Self review
- State the equation for the area of a circular culture or clear zone.
- Why should two perpendicular diameters be measured for an uneven zone?
- A colony has a diameter of 12 mm12\,\mathrm{mm}12mm. Calculate its area.
- Explain why comparing diameters alone can be misleading.
