AQA · Mathematics · 8300
GCSE Maths: Circles: perimeter – semi-circle
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Circles: perimeter – semi-circle (Corbettmaths Video 62), 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 two components make up the perimeter of a semi-circle?
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The curved arc (half the circumference of a full circle) plus the diameter.
What is the formula for the perimeter of a semi-circle with diameter d?
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πd/2 + d, which can also be written as d(π/2 + 1) or approximately 2.571d.
What is the formula for the perimeter of a semi-circle with radius r?
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πr + 2r, which can also be written as r(π + 2) or approximately 5.142r.
What two components make up the perimeter of a quarter-circle?
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The curved arc (one-quarter of the circumference) plus two radii (the two straight edges).
What is the formula for the perimeter of a quarter-circle with radius r?
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πr/2 + 2r, which can also be written as r(π/2 + 2) or approximately 3.571r.
Why must the diameter be included when calculating a semi-circle's perimeter?
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The diameter is the straight edge of the semi-circle that forms part of its boundary. Without it, you only have the curved arc, not the complete perimeter.
The perimeter of a quarter-circle with radius r is ?.
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πr/2 + 2r
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