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Circles, arcs and sectors
Every circle calculation uses π. Arcs and sectors are just fractions of a whole circle.
Circumference and area
C = πd = 2πr
A = πr2
If you are given the diameter, halve it to get the radius for area.
A = πr2
If you are given the diameter, halve it to get the radius for area.
Arcs and sectors
A sector with angle θ is θ360 of the circle.
Arc length = θ360 × 2πr
Sector area = θ360 × πr2
Arc length = θ360 × 2πr
Sector area = θ360 × πr2
Exact answers
"Leave your answer in terms of π" means do not multiply out π.
A circle with r = 5: area = 25π cm2.
A circle with r = 5: area = 25π cm2.
Find the area of a sector of radius 6 cm with angle 60°. Give your answer to 1 d.p.
- 60360 × π × 62
- = 16 × 36π = 6π
- = 18.8 cm2
Answer: 18.8 cm2
C = πd, A = πr2. Arcs and sectors take the fraction θ ÷ 360 of the circumference or area. In terms of π means keep π as a symbol.
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