IGCSE Math RevisionWorked example 1: Area of a circle
Find the area of a circle of radius 4.2 cm.
Solution
- \(A=\pi r^2=\pi\times17.64\).
- \(=55.4\) cm² (3 s.f.).
Answer: 55.4 cm²
Tip: Square the radius, not the diameter.
Edexcel IGCSE Maths (4MA1) · Unit 5: Geometry
IGCSE Maths Circles, Arcs and Sectors Questions and Answers
Circles, Arcs and Sectors questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 2 worked examples first, then try the 3 exam-style questions yourself and check your working against the mark scheme.
- 2 worked examples
- 3 questions with mark schemes
- Higher tier · calculator allowed
- Free, no sign-in
What this topic covers
- Circles 1: Circumference & Area: Circumference and area of circles, including working backwards to the radius.
- Arcs, Sectors & Segments: Arc lengths, sector areas and segment areas of circles.
Circles, Arcs and Sectors worked examples
Worked example 2: Arc length and sector area
A sector has radius 12 cm and angle \(75^\circ\). Find its arc length and area.
Solution
- Arc \(=\tfrac{75}{360}\times2\pi\times12=15.7\) cm.
- Area \(=\tfrac{75}{360}\times\pi\times144=94.2\) cm².
Answer: 15.7 cm; 94.2 cm²
Tip: The fraction of the circle is angle/360.
Circles, Arcs and Sectors exam-style questions
Try each question before you open the answer. The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.
Question 1
A circle has radius 6.5 cm. Work out its circumference. Give your answer to 3 significant figures.
Show the answer and mark scheme
- M1 2 × π × 6.5 or π × 13
- A1 40.8 (40.84…)
Answer: 40.8 cm
Question 2
A circle has an area of 80 cm². Work out its radius. Give your answer to 3 significant figures.
Show the answer and mark scheme
- M1 πr² = 80 or r = √(80 ÷ π)
- A1 5.05 (5.046…)
Answer: 5.05 cm
Question 3
A bicycle wheel has diameter 65 cm. How many complete turns does the wheel make when the bicycle travels 1 km?
Show the answer and mark scheme
- M1 circumference π × 65 (= 204.2… cm)
- M1 100 000 ÷ their 204.2 (consistent units)
- A1 489
Answer: 489 complete turns
Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.
Revise circles, arcs and sectors for the exam
- Unit 5 practice: Geometry in the student hub (more questions with mark schemes)
- IGCSE Maths revision notes for this topic and the IGCSE Maths formula sheet
- Edexcel IGCSE Maths 4MA1 past papers to practise under exam conditions
- IGCSE Maths 4MA1 examiner report summary: where students lose marks
Questions students ask
Which Edexcel IGCSE Maths papers test circles, arcs and sectors?
Either Higher tier paper, 1H or 2H, can test circles, arcs and sectors: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.
Where can I practise more circles, arcs and sectors questions?
In the IGCSE student hub: Unit 5 (Geometry) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.
More Unit 5 topics: Geometry
- Angles and Polygons questions
- Quadrilaterals and Symmetry questions
- Congruent Triangles questions
- Bearings and Constructions questions
- Area and Perimeter questions
- Volume and Surface Area questions
- Pythagoras' Theorem questions
- Right-Angled Trigonometry questions
- Sine and Cosine Rules questions
- Transformations questions
- Similar Shapes questions
- Circle Theorems questions