How do you find the area and circumference of a circle?
Short answer
Area of a circle = πr², where r is the radius. Circumference = 2πr, or πd where d is the diameter. Always check whether you are given the radius or the diameter: the radius is half the diameter. Area is in square units, circumference in ordinary units.
Step by step
- Find the radius. If you are given the diameter, halve it.
- For the area, square the radius first, then multiply by π.
- For the circumference, multiply the diameter by π.
- Round as the question asks and give the units: cm² for area, cm for circumference.
Worked example
A circle has a diameter of 10 cm
- r = 10 ÷ 2 = 5 cm
- Area = π × 5² = 25π = 78.5 cm² (1 d.p.)
- Circumference = π × 10 = 31.4 cm (1 d.p.)
Common mistakes
- Using the diameter in πr².
- Working out (πr)² instead of π × r².
- Mixing up the two formulas. Area has the square, because area is measured in square units.
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