Circles - circumference and area
Cambridge IGCSE Mathematics (0580) · Unit 5: Mensuration · 9 flashcards
Circles - circumference and area is topic 5.2 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 5 — Mensuration , alongside Perimeter and area, Surface area and Volume. In one line: The circumference is the distance around the circle. It can be calculated using the formula C = 2πr or C = πd, where r is the radius and d is the diameter.
This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.
The deck below contains 9 flashcards — 3 definitions and 1 key concept — covering the precise wording mark schemes reward. Use the 3 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.
The circumference of a circle
The circumference is the distance around the circle. It can be calculated using the formula C = 2πr or C = πd, where r is the radius and d is the diameter.
Questions this Circles - circumference and area deck will help you answer
- › What is 'π' (pi) and what does it represent in relation to a circle?
Define the circumference of a circle.
The circumference is the distance around the circle. It can be calculated using the formula C = 2πr or C = πd, where r is the radius and d is the diameter.
State the formula for the area of a circle.
The area of a circle is the amount of space enclosed within the circle. The formula is A = πr², where r is the radius.
A circle has a radius of 7 cm. Calculate its circumference. (Use π = 3.142)
C = 2πr = 2 × 3.142 × 7 = 43.988 cm. Therefore, the circumference is approximately 43.99 cm (to 2 d.p.).
A circle has a diameter of 10 cm. Find its area (Use π = 3.142)
The radius is half the diameter, so r = 5 cm. A = πr² = 3.142 × 5² = 78.55 cm². The area is 78.55 cm².
What is 'π' (pi) and what does it represent in relation to a circle?
Pi (π) is a mathematical constant approximately equal to 3.142. It represents the ratio of a circle's circumference to its diameter.
Define the terms 'radius' and 'diameter' of a circle and the relationship between them.
The radius (r) is the distance from the center of the circle to any point on its circumference. The diameter (d) is the distance across the circle passing through the center. d = 2r.
A sector of a circle has an angle of 60° at the center and a radius of 5 cm. What fraction of the whole circle is the sector?
The fraction of the circle is the angle of the sector divided by 360°. So, the fraction is 60/360 = 1/6.
A sector has a central angle of 90° in a circle of radius 4cm. Calculate the sector area. (Use π = 3.142)
The area of a sector = (θ/360) x πr². Therefore, area = (90/360) x 3.142 x 4² = (1/4) x 3.142 x 16 = 12.568 cm²
An arc has a central angle of 45° in a circle with radius 8 cm. Calculate the arc length. (Use π = 3.142)
Arc length = (θ/360) x 2πr. Therefore, arc length = (45/360) x 2 x 3.142 x 8 = (1/8) x 50.272 = 6.284 cm.
Key Questions: Circles - circumference and area
Define the circumference of a circle.
The circumference is the distance around the circle. It can be calculated using the formula C = 2πr or C = πd, where r is the radius and d is the diameter.
State the formula for the area of a circle.
The area of a circle is the amount of space enclosed within the circle. The formula is A = πr², where r is the radius.
Define the terms 'radius' and 'diameter' of a circle and the relationship between them.
The radius (r) is the distance from the center of the circle to any point on its circumference. The diameter (d) is the distance across the circle passing through the center. d = 2r.
More topics in Unit 5 — Mensuration
Circles - circumference and area sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.
Cambridge syllabus keywords to use in your answers
These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.
Key terms covered in this Circles - circumference and area deck
Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.
Related Mathematics guides
Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.
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