Edexcel GCSE Maths (1MA1), Higher tier · Geometry and measures
Practise Arcs and sectors. 1 exam-style questions plus unlimited generated ones on this subtopic, at up to four difficulty levels, with full mark schemes and a progress tracker. Free, no account needed.
Written for this site in the style of Edexcel exam questions. They are not taken from real past papers.
Question 1Easy2 marks
The diagram shows a sector of a circle, centre \(O\). The radius of the circle is 15 cm and the angle of the sector is 32°. Diagram NOT accurately drawn
[object Object]
Work out the area of the sector. Give your answer correct to 1 decimal place.[2]
Show the answer and mark scheme
Answer: \(62.8\) cm²
M1 for \(\frac{32}{360} \times \pi \times 15^2\)
A1 for 62.8 (62.83...)
Worked solution: Area \(= \frac{32}{360} \times \pi \times 15^2\) \(= 62.83\ldots\) = 62.8 cm² (1 d.p.)
Question 2Medium3 marks
The diagram shows a sector of a circle, centre \(O\). The radius of the circle is 9 cm. The area of the sector is \(54\pi \) cm². Diagram NOT accurately drawn
[object Object]
Work out the size of the angle marked \(x\).[3]
Show the answer and mark scheme
Answer: \(240^\circ\) °
M1 for \(\frac{x}{360} \times \pi \times 9^2 = 54\pi \)
M1 for \(x = 54\pi \times \frac{360}{81\pi}\)
A1 for 240
Worked solution: \(\frac{x}{360} \times 81\pi = 54\pi \), so \(x = 360 \times \frac{54\pi }{81\pi} = 240\).
Question 3Hard4 marks
The diagram shows a sector of a circle, centre \(O\). The angle of the sector is 107° and the length of the arc is 10.3 cm. Diagram NOT accurately drawn
[object Object]
Work out the area of the sector. Give your answer correct to 3 significant figures.[4]
Show the answer and mark scheme
Answer: \(28.4\) cm²
M1 for \(\frac{107}{360} \times 2\pi r = 10.3\)
A1 for \(r = 5.515\ldots\)
M1 for \(\frac{107}{360} \times \pi \times r^2\) using their \(r\)
A1 for 28.4 (28.40...)
Worked solution: \(\frac{107}{360} \times 2\pi r = 10.3\) so \(r = \frac{10.3 \times 360}{214\pi} = 5.515\ldots\) cm. Area \(= \frac{107}{360} \times \pi \times 5.515\ldots^2 = 28.40\ldots\) = 28.4 cm² (3 s.f.)