Circumference and area

Objective. Calculate circle measures in terms of π and as decimals.

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2. Worked example
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Learn: the key idea

Circumference and area formulas let you calculate circle measures from the radius or diameter, using circumference = πd (or 2πr) and area = πr². Leaving π in the answer gives an exact value, while using 3.14 or a calculator's π key gives a rounded decimal. For a circle of radius 5 cm, the circumference is 2 × π × 5 = 10π cm ≈ 31.4 cm, and the area is π × 5² = 25π cm² ≈ 78.5 cm². Always check whether a question gives the radius or the diameter before substituting into a formula.

Worked example

Calculate the area of a circle with diameter 14 cm, giving your answer in terms of π.

1 $Find the radius: 14 \div 2 = 7 cm$
2 $Recall the formula: area = πr²$
3 $Substitute the radius: π \times 7²$
4 $The area is 49π cm²$

Answer: 49π cm²

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Common mistake. Pupils often use the diameter directly in the area formula instead of halving it first, squaring the diameter rather than the radius. Always halve the diameter to find the radius before calculating area.

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