5.2

Circles - circumference and area

9 flashcards to master Circles - circumference and area

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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.

About Circles - circumference and area (5.2)

These 9 flashcards cover everything you need to know about Circles - circumference and area for your Cambridge IGCSE Mathematics (0580) exam. Each card is designed based on the official syllabus requirements.

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