5.2

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.

Key definition

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

Definition Flip

Define the circumference of a circle.

Answer Flip

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.

Definition Flip

State the formula for the area of a circle.

Answer Flip

The area of a circle is the amount of space enclosed within the circle. The formula is A = πr², where r is the radius.

Key Concept Flip

A circle has a radius of 7 cm. Calculate its circumference. (Use π = 3.142)

Answer Flip

C = 2πr = 2 × 3.142 × 7 = 43.988 cm. Therefore, the circumference is approximately 43.99 cm (to 2 d.p.).

Key Concept Flip

A circle has a diameter of 10 cm. Find its area (Use π = 3.142)

Answer Flip

The radius is half the diameter, so r = 5 cm. A = πr² = 3.142 × 5² = 78.55 cm². The area is 78.55 cm².

Key Concept Flip

What is 'π' (pi) and what does it represent in relation to a circle?

Answer Flip

Pi (π) is a mathematical constant approximately equal to 3.142. It represents the ratio of a circle's circumference to its diameter.

Definition Flip

Define the terms 'radius' and 'diameter' of a circle and the relationship between them.

Answer Flip

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.

Key Concept Flip

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?

Answer Flip

The fraction of the circle is the angle of the sector divided by 360°. So, the fraction is 60/360 = 1/6.

Key Concept Flip

A sector has a central angle of 90° in a circle of radius 4cm. Calculate the sector area. (Use π = 3.142)

Answer Flip

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

Key Concept Flip

An arc has a central angle of 45° in a circle with radius 8 cm. Calculate the arc length. (Use π = 3.142)

Answer Flip

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.

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5.1 Perimeter and area 5.3 Surface area

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.

circumference area of circle pi radius diameter sector area arc length fraction of circle

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.

The circumference of a circle
Formula for the area of a circle
The terms 'radius' and 'diameter' of a circle and the relationship between them

Related Mathematics guides

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How to study this Circles - circumference and area deck

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