Circles
Two formulas
The radius r goes from the centre to the edge.
The diameter d goes right across, so d = 2r.
circumference C = πd = 2πr
area A = πr²
- a circle has diameter 10 cm, so r = 5 cm
- C = π × 10 = 31.4159... = 31.4 cm (3 s.f.)
- A = π × 5² = 25π = 78.5398... = 78.5 cm² (3 s.f.)
Keep the full calculator value until the last step, then round.
In terms of π
"Give your answer in terms of π" means leave π as a letter: the area above is 25π cm², which is exact.
Work out the number in front of π: π × 5² = 25π.
Parts of a circle
A semicircle is half a circle, a quarter circle is a quarter.
Their perimeter has straight edges as well as the curved part.
Not drawn accurately
- curved part = ½ × π × 8 = 12.566...
- perimeter = 12.566... + 8 = 20.566... = 20.6 cm (3 s.f.)
The most common slip: forgetting the straight edge, or using the diameter where the formula needs the radius.
Check on the calculator
Choose a radius, say 6. Work out 2 × π × 6 and π × 6². Then double the radius to 12 and work them out again. The circumference doubles; what happens to the area?
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This question is in Brainlag Plus