Cambridge IGCSE · Mathematics (0580)

Circles, arcs and sectors: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Circles, arcs and sectors.

10 questions24 marksFree, no account

Question 1

1 mark

A semicircle has a diameter of 14 cm. Calculate the total perimeter of the semicircle. Use \( \pi = \frac{22}{7} \).

Question 2

1 mark

A sector of a circle has a central angle of \( 60^\circ \) and an arc length of \( 6\pi \) cm. Find the radius of the circle.

Question 3

1 mark

The area of a sector is \(12\pi \text{ cm}^2\). If the angle of the sector is \(108^\circ\), find the radius of the sector.

Question 4

1 mark

A circle has a diameter of \(12\) cm. Calculate its area, giving your answer in terms of \(\pi\).

Question 5

1 mark

In a circle with centre \(O\) and radius \(9\) cm, a sector has a central angle of \(120^\circ\). Calculate the length of the arc of this sector, giving your answer in terms of \(\pi\).

Question 6

2 marks

A semicircle has a radius of 4 cm. Calculate its area, giving your answer in terms of \( \pi \).

Write your answer out first, then check it against the worked solution.

Question 7

3 marks

A circle has a radius of \(r\) cm. If the area of the circle is numerically equal to its circumference, calculate the value of \(r\).

Write your answer out first, then check it against the worked solution.

Question 8

5 marks

A sector of a circle has a radius of \(10 \text{ cm}\) and an angle of \(108^\circ\). Calculate the perimeter of the sector. Give your answer correct to 3 significant figures.

Write your answer out first, then check it against the worked solution.

Question 9

4 marks

A circle has a radius of 12 cm. A sector of this circle has a central angle of \( 60^\circ \).

(a) Calculate the circumference of the circle, giving your answer in terms of \( \pi \).

(b) Calculate the area of the circle, giving your answer in terms of \( \pi \).

(d) Calculate the area of the sector, giving your answer in terms of \( \pi \).

Write your answer out first, then check it against the worked solution.

Question 10

5 marks

The diagram shows a circle with centre \(O\) and radius \(10 \text{ cm}\). A chord \(AB\) is \(12 \text{ cm}\) long.
(a) Calculate the perpendicular distance from the centre \(O\) to the chord \(AB\).

(b) Calculate the angle \(AOB\) in degrees. Give your answer correct to one decimal place.

(c) Calculate the area of the minor segment cut off by the chord \(AB\). Give your answer correct to 3 significant figures.

Write your answer out first, then check it against the worked solution.

* The content provided by thinka is generated by AI and may not always be accurate or up-to-date. Please use it as a supplementary resource and verify with official materials.

You've seen the model answer. Now get yours marked.

This page can show you how a good answer looks. It cannot tell you what your answer was missing. thinka marks your written work against the real mark scheme in about 15 seconds.

Get My Answers Marked Back to the notes

Want more questions like these? Get a fresh set on this topic, graded as you go.

Practice More