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Cross-sectional areas of bacterial cultures and clear agar jelly

When bacteria are grown on agar jelly in a Petri dish, a culture or a clear zone usually forms a circle. To compare them fairly you calculate the cross-sectional area of each circle using the formula area = πr2, where r is the radius. At GCSE you use π = 3.14 unless told otherwise.

Measuring across the middle of a circle gives you the diameter, not the radius. The radius is half the diameter, so always halve your measurement first, then square it, then multiply by π. Forgetting to halve is the most common mistake.

Worked example: a clear zone around an antibiotic disc has a diameter of 20 mm. Its radius is 10 mm, so its area is 3.14 × 10 × 10 = 314 mm2. A bacterial colony with a diameter of 6 mm has a radius of 3 mm, so its area is 3.14 × 3 × 3 = 28 mm2 to the nearest whole number.

A clear zone means the bacteria in that region have been killed or stopped from growing. The larger the clear area, the more effective the antiseptic, antibiotic or plant extract. Areas from a class experiment are often compared in a results table, for example 50 mm2, 113 mm2 and 314 mm2.

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