26 self-marking GCSE and IGCSE practice questions on Arc length, written specifically for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Foundation and Higher and Core and Extended tier. Instant marking with full worked solutions on every question.
A few of the 26 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.
Question 12 marksGrade 4-5
The diagram shows a sector of a circle with centre O and radius 12 cm. The angle at the centre is 270°. Work out the length of the arc. Give your answer correct to 3 significant figures.
What are the common mistakes in Arc length?
When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.
Confuses radius and diameter when calculating an arc length or sector area
Used the diameter (12 cm) instead of the radius (6 cm) in the arc length formula.
Calculates the arc length as if for the whole circle, forgetting to take the fraction given by the angle
Calculated the full circumference 2π×12≈75.4
Quick answers about Arc length
How many Arc length practice questions are there?
There are 26 self-marking GCSE and IGCSE Maths questions on Arc length, written for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Foundation and Higher and Core and Extended tier. Each one is marked instantly and has a full worked solution.
Do I need an account to practise Arc length?
No. You can start practising Arc length straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.
Show the worked solution
Arc length =360270×2π×12M1
=18π≈56.549 cm ≈56.5 cm (3 s.f.) A1
Question 22 marksGrade 5-6
AOB is a sector of a circle, centre O, radius 6 cm. The angle at the centre, angle AOB, is 50°.
Show that the length of arc AB is 5.24 cm, correct to 3 significant figures.
A sector of a circle has centre O and radius 15 cm. The arc length of the sector is 86.39 cm. Work out the angle at the centre of the sector. Give your answer correct to the nearest degree.
Question 43 marksGrade 7-8
OAB is a sector of a circle with centre O and radius 8 cm.
The length of the arc AB is 4π cm.
Work out, in terms of π, the area of the sector. Give your answer in its simplest form.
Question 54 marksGrade 8-9
A shape is made by removing a smaller sector (radius r cm, centre O) from a larger sector (radius OC, centre O). Both sectors have an angle of 60°.
The ratio of radius OA (=r) to radius OC is 2:3.
Work out, in terms of π and r, the total length of arc AB (the smaller sector's arc) and arc CD (the larger sector's arc). Give your answer in its simplest form.