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Area and circumference Quiz

Grade 3 • 3R • 10 Questions (34 Marks)

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Score: 0 / 10
Area and circumference — Notes & Worked Examples Show / Hide

Explanation:

For any circle with radius r and diameter d = 2r: the Circumference (perimeter) is C = πd (or 2πr), and the Area is A = πr². Always check whether the question gives you the radius or the diameter before starting!

If the question asks for your answer in terms of π (non-calculator), leave π as a symbol in your answer (e.g. 25π cm²). Remember that the perimeter of a semicircle includes the straight diameter as well as the curved arc: Perimeter = 12πd + d.

Example 1: A circle has a diameter of 12 cm. Work out its area and circumference to 1 d.p.

d = 12 cm r = 6
r = 12 ÷ 2 = 6 cm
A = π × 6² = 113.1 cm²
C = π × 12 = 37.7 cm

Example 2: Work out the perimeter of a semicircle with radius 5 cm. Give your answer to 1 d.p.

r = 5 cm d = 10 cm
d = 2 × 5 = 10 cm
Arc = 12π(10) = 15.71 cm
15.71 + 10 = 25.7 cm
Question 1
[2 marks]
6mm
Calculate the area of the circle
Give your answer to 1 decimal place
mm²
Worked Solution & Answer
(The area of a circle is πr²) B1
Answer: 113.1 mm2 mm²
Question 2
[2 marks]
12mm
Calculate the circumference of the circle
Give your answer to 1 decimal place
mm
Worked Solution & Answer
(The circumference of a circle is π × diameter = 2πr) B1
Answer: 37.7 mm mm
Question 3
[2 marks]
The centre of this circle is marked with a cross (×).
(a) Write down the mathematical name of the straight line shown in the circle. [1 mark]
(b) Write down the mathematical name of the straight line that is touching the circle. [1 mark]
Worked Solution & Answer
(a)
Line from centre to circumference is a radius B1
Answer (a): Radius
(b)
Line touching circle at one point is a tangent B1
Answer (b): Tangent
Question Paper (PDF) • Mark Scheme (PDF)
Question 4 IGCSE Nov 2023 1F Q19 / 1H Q5
[3 marks]
The diagram shows a shaded shape made from three identical semicircles, X, Y and Z.
ABCDEXYZDiagram NOTaccurately drawn
ABCDE is a straight line.
AC is the diameter of semicircle X and B is the centre of semicircle X
BD is the diameter of semicircle Y and C is the centre of semicircle Y
CE is the diameter of semicircle Z and D is the centre of semicircle Z
AC = BD = CE = 20 cm
Work out the perimeter of the shaded shape.
Give your answer correct to the nearest whole number.
cm
Worked Solution & Answer
Each semicircle arc = ½ × π × 20 = 10π ≈ 31.416 cm M1
Straight segments AB = 10 cm and DE = 10 cm M1
Perimeter = 3 × 10π + 10 + 10 = 30π + 20 = 114.247... ≈ 114 cm. A1
Answer: 114 cm
Question Paper (PDF) • Mark Scheme (PDF)
Question 5 IGCSE Jan 2021 1F Q24 / 1H Q8
[3 marks]
The region, shown shaded in the diagram, is a path.
O2 m7 mDiagram NOTaccurately drawn
The boundary of the path is formed by two semicircles, with the same centre O, and two straight lines.
The inner semicircle has a radius of 7 metres.
The path has a width of 2 metres.
Work out the perimeter of the path.
Give your answer correct to one decimal place.
m
Worked Solution & Answer
Inner arc = π × 7 = 7π ≈ 21.991 m M1
Outer radius = 7 + 2 = 9 m, outer arc = π × 9 = 9π ≈ 28.274 m M1
Total perimeter = 7π + 9π + 2 + 2 = 16π + 4 = 54.265... ≈ 54.3 m. A1
Answer: 54.3 m m
Question Paper (PDF) • Mark Scheme (PDF)
Question 6 OCR Jun 2025 3F Q1
[3 marks]
The diagram shows a circle, centre O, and a straight line.
O
(a) the straight line [1 mark]
(b) the perimeter of the circle. [1 mark]
(b) On the diagram, draw a diameter. [1 mark]
Worked Solution & Answer
(a)
A straight line joining two points on the circumference is a chord. B1
Answer (a): Chord
(b)
The perimeter of a circle is called the circumference. B1
Answer (b): Circumference
(b)
Draw a straight line passing through O from one side of the circumference to the other. B1
Answer (b): Straight line drawn through centre O joining two points on the circumference
Question Paper (PDF) • Mark Scheme (PDF)
Question 7 AQA Jun 2019 1F Q25 / 1H Q9
[4 marks]
A shaded semicircle is inside a circle as shown.
Not drawnaccurately10 cm8 cm
How many times bigger is the unshaded area than the shaded area?
The radius of the circle is 10 cm
The diameter of the semicircle is 8 cm
Answer
Worked Solution & Answer
(The area of a semicircle is ½ × π × r²)
Area of circle = π × 102 = 100π M1
Radius of semicircle = 8 ÷ 2 = 4 cm M1
Area of shaded semicircle = 12 × π × 42 = 8π M1
Unshaded area = 100π - 8π = 92π
Ratio = 92π8π = 928 = 11.5 A1
Answer: Answer 11.5
Question Paper (PDF) • Mark Scheme (PDF)
Question 8
[5 marks]
A farmer has a field in the shape of a semicircle of diameter 50 m.
50 mThe farmer asks Jim to build a fence around the edge of the field.Jim tells him how much it will cost.
Total cost = £29.86 per metre of fence plus £180 for each day’s work
£
Worked Solution & Answer
Arc length = 0.5 × π × 50 = 78.5398 m M2
Total perimeter = 78.5398 + 50 = 128.5398 m M1
Fence cost = 128.5398 × 29.86 = £3838.20 M1
Total cost = 3838.20 + 3 × 180 = £4378.20 A1
Answer: £ 4378.20
Question Paper (PDF) • Mark Scheme (PDF)
Question 9 IGCSE Nov 2021 1F Q16
[5 marks]
The diagram shows the front of a wooden door with a semicircular glass window.
0.5 m2 m0.75 mDiagram NOTaccurately drawn
Julie wants to apply 2 coats of wood varnish to the front of the door, shown shaded in the diagram.
250 millilitres of wood varnish covers 4 m2 of the wood.
Work out how many millilitres of wood varnish Julie will need.
Give your answer correct to the nearest millilitre.
millilitres
Worked Solution & Answer
Area of door = 2 × 0.75 = 1.5 m² M1
Area of semicircle = ½ × π × 0.25² = 0.09817... m² M1
Wood area = 1.5 – 0.09817... = 1.4018... m² M1
Two coats = 2.80365... m² M1
Varnish needed = (2.80365... ÷ 4) × 250 = 175.228... = 175 ml A1
Answer: 175 millilitres
Question Paper (PDF) • Mark Scheme (PDF)
Question 10
[5 marks]
Balena has a garden in the shape of a circle of radius 10 m.
He is going to cover the garden with grass seed to make a lawn.
Grass seed is sold in boxes.
Each box of grass seed will cover 46 m2 of garden.
10 m
Balena wants to cover all the garden with grass seed.
(a) Work out an estimate for the number of boxes of grass seed Balena needs.
You must show your working. [4 marks]
(b) Is your estimate for part (a) an underestimate or an overestimate?
Give a reason for your answer. [1 mark]
Worked Solution & Answer
(a)
Area = π × 10² ≈ 3 × 100 = 300 m² M3
Boxes ≈ 300 ÷ 50 = 6 (or 314 ÷ 45 ≈ 7) A1
Answer (a): 6 to 8
(b)
Underestimate because 3 < π and 50 > 46 C1
Answer (b): Underestimate, because 3 was used for π (less than 3.14...) and 50 was used for 46 (greater than 46), giving a smaller value
Question Paper (PDF) • Mark Scheme (PDF)
Score: 0 / 10 (0 / 34 marks)
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Grade 3 Quizzes

24 Topics
3A - Error intervals3B - Operations with fractions
3C - Estimation3D - Writing and simplifying ratio
3E - Ratio3F - Proportion recipes
3G - Percentages3H - Percentage change
3J - Exchange rates3K - Conversions and units
3L - Scale drawings3M - Best buy questions
3N - Substitution3P - Solving linear equations
3Q - Straight line graphs3R - Area and circumference
3S - Rotations3T - Reflections
3U - Enlargements3V - Translations
3W - Mixed transformations3X - Area of compound shapes
3Y - Frequency trees3Z - Two way tables