AQA · Mathematics · 8300
GCSE Maths: Circles: arc length
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Circles: arc length (Corbettmaths Video 58), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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What is the formula for the arc length of a sector?
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Arc length = (θ/360) × 2πr, where θ is the angle in degrees and r is the radius.
What is the perimeter of a sector?
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Perimeter of sector = arc length + 2r, where r is the radius. It includes the curved arc and both straight radii.
What is the arc length of a quarter circle with radius r?
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(πr)/2 or 0.5πr. A quarter circle has an angle of 90°, so arc length = (90/360) × 2πr = πr/2.
What is the perimeter of a quarter circle with radius r?
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2r + (πr)/2 or r(2 + π/2). It consists of the arc length πr/2 plus two radii of length r each.
If you know the arc length and radius of a sector, how can you find the central angle?
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Rearrange the arc length formula: θ = (arc length × 360)/(2πr) or θ = (arc length × 180)/(πr).
When giving arc length answers 'in terms of π', what does this mean?
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Leave π as a symbol in the answer rather than multiplying by its decimal approximation (e.g., write 5π cm instead of 15.7 cm).
If you know the perimeter and radius of a sector, how can you find the arc length?
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Arc length = Perimeter - 2r. Subtract the two radii from the total perimeter.
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