Circle calculations
Objective. Solve multi-step area and circumference problems.
- 1. Learn
- 2. Worked example
- 3. Practice
- 4. Feedback
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Learn: the key idea
Circle calculations involve finding the area (A = πr²) or circumference (C = 2πr or πd) of a circle, often as part of a multi-step problem such as finding the area of a composite shape or working backwards from a given area to find the radius. For a multi-step problem, identify first whether the question wants area or circumference, substitute the known radius or diameter carefully, and keep π exact or rounded as instructed. For example, a circle with radius 4 cm has area π × 4² = 16π ≈ 50.3 cm² and circumference 2π × 4 = 8π ≈ 25.1 cm. Composite shape problems often require adding or subtracting a circular region from a rectangle or another circle.
Worked example
A circular pond has a diameter of 14 m. Calculate its area, giving your answer to 1 decimal place.
- 1Since the formula uses radius, halve the diameter: r = 14 ÷ 2 = 7 m.
- 2Use the formula A = πr².
- 3Substitute: A = π × 7² = π × 49.
- 4A ≈ 49 × 3.14159 ≈ 153.9 m².
Answer: 153.9 m² (1 d.p.)
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Practice
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Start practisingCommon mistake. Pupils often use the diameter instead of the radius in the area formula, calculating π × d² rather than π × r², which gives an answer four times too large. Always confirm whether the given measurement is a radius or a diameter before substituting.
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