IGCSE Math RevisionQuestion 1
A circle has a radius of \(7\) cm.
Work out its circumference, correct to 3 significant figures.
Show the worked answer
- \(C = 2\pi r = 2 \times \pi \times 7 = 43.98\ldots\) cm
Answer: \(44.0\) cm
Cambridge IGCSE Maths (0580) · Topic 5: Mensuration · 5.3
Cambridge IGCSE Maths 0580 Circles, Arcs and Sectors Questions
Circles, Arcs and Sectors questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.
- 10 questions
- 7 Core
- 3 Extended
- 1 non-calculator
- Free, no sign-in
What the syllabus asks
- 5.3 Circles, arcs and sectors Core Extended
Circumference and area of a circle; Arc length and sector area as fractions of the circle, where the sector angle is a factor of 360°.
Extended also: Arc length and sector area for any angle, including major and minor sectors, and finding the angle or radius from them.
Summarised in our own words: check the exact wording in the official 0580 syllabus.
Circles, Arcs and Sectors questions: Core
For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).
Question 2
A circle has a diameter of \(10\) cm.
Work out its area, correct to 3 significant figures.
Show the worked answer
- Radius \(= 5\) cm.
- \(A = \pi r^2 = \pi \times 25 = 78.53\ldots\) cm²
Answer: \(78.5\) cm²
Question 3
A circle has diameter 14 cm. Find its area. Give your answer correct to 3 significant figures.
Show the answer and mark scheme
- M1 π × 7²
- A1 154 cm² (153.9…)
Answer: \(154\text{ cm}^2\)
Question 4
A semicircle has a radius of \(6\) cm.
Work out its perimeter, correct to 3 significant figures.
Show the worked answer
- Curved part: half of \(2\pi \times 6\), which is \(6\pi = 18.84\ldots\) cm.
- Add the diameter, \(12\) cm: \(30.84\ldots\) cm.
Answer: \(30.8\) cm
Question 5
A sector of a circle of radius \(8\) cm has an angle of \(90°\).
Work out its area, correct to 3 significant figures.
Show the worked answer
- \(90°\) is \(\frac{1}{4}\) of the circle.
- \(\frac{1}{4} \times \pi \times 64 = 16\pi = 50.26\ldots\) cm²
Answer: \(50.3\) cm²
Question 6
A sector has radius 12 cm and angle \(60^\circ\). Find its arc length in terms of \(\pi\).
Show the answer and mark scheme
- M1 60/360 × 2 × π × 12
- A1 4π cm
Answer: \(4\pi\) cm
Question 7
The circumference of a circle is 50 cm. Find its radius. Give your answer correct to 3 significant figures.
Show the answer and mark scheme
- M1 50 ÷ (2π)
- A1 7.96 cm (7.957…)
Answer: \(7.96\) cm
Circles, Arcs and Sectors questions: Extended
Extended content, for Papers 2 and 4. Core students can skip these.
Question 8
A sector has radius \(9\) cm and angle \(140°\).
Work out its arc length, correct to 3 significant figures.
Show the worked answer
- Arc length \(= \frac{140}{360} \times 2\pi \times 9 = 7\pi = 21.99\ldots\) cm
Answer: \(22.0\) cm
Question 9
A sector of a circle of radius \(10\) cm has an area of \(60\) cm².
Find the angle of the sector, correct to 1 decimal place.
Show the worked answer
- \(\frac{\theta}{360} \times \pi \times 100 = 60\)
- \(\theta = \frac{60 \times 360}{100\pi} = 68.75\ldots°\)
Answer: \(68.8°\)
Question 10
The circumference of a circle is \(50\) cm.
Work out its area, correct to 3 significant figures.
Show the worked answer
- \(2\pi r = 50\), so \(r = \frac{50}{2\pi} = 7.957\ldots\) cm.
- \(A = \pi r^2 = 198.9\ldots\) cm²
Answer: \(199\) cm²
Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).
Keep going
- Mensuration practice for 0580: more questions, each one marked, tagged Core or Extended
- My mistakes, then a Skill Builder on the skills you missed
- Common mistakes in 0580: what the Cambridge examiner reports say
- Mensuration revision notes and the 0580 formula sheet
- Cambridge IGCSE Maths 0580 past papers, when you are ready for a full paper
Questions students ask
Which Cambridge 0580 papers can test circles, arcs and sectors?
Circles, Arcs and Sectors is on both tiers (syllabus 5.3), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.
Are these Cambridge past-paper questions?
No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.
Where can I practise more circles, arcs and sectors questions?
In the 0580 practice for topic 5 (Mensuration), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.