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Sector areas and arc lengths

Free Printable Sector areas and arc lengths PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 5)

Download free sector areas and arc lengths worksheets (PDF), GCSE maths past paper questions and worked solutions for Sector areas and arc lengths (5M). This is a Grade 5 geometry topic from the GCSE questions by topic collection for Foundation and Higher tier crossover GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from IGCSE MT, Maths Genie, Maths4Everyone, Corbett Maths, Maths Made Easy, Dr Frost, Naiker Maths, M4ths.com, Dr. Austin, 1st Class Maths, Metatutor, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our sector areas and arc lengths revision notes and worked examples with diagrams, try real GCSE past paper sector areas and arc lengths questions with step-by-step solutions, or download a PDF of all sector areas and arc lengths worksheet links.

Free Sector areas and arc lengths PDF Worksheets & Answers

Grade 5 • Topic 5M
Resource Questions Answers
GCSE past paper questions & solutions
 Qs Ans
IGCSE (9–1) past paper booklet
 Qs Ans
Graded exam questions & solutions
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GCSE 9–1 practice booklet & solutions
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Practice Questions & answers
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Textbook Exercise & answers
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MME worksheet & model answers
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GCSE worksheet & solutions
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Exam question booklet & solutions
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GCSE worksheet & answers
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Dr. Austin (1)
Sector areas and arc lengths questions & answers
 Qs Ans
Dr. Austin (2)
Sector areas and arc lengths questions & answers
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Dr. Austin (3)
Sector areas and arc lengths questions & answers
 Qs Ans
Edexcel exam questions & solutions
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AQA exam questions & solutions
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Topic worksheet & worked solutions
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GCSE topic booklet & answers
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PMT (Edxl)
Edexcel GCSE topic questions & solutions
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PMT (AQA)
AQA GCSE topic questions & solutions
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PMT (IGCSE)
Edexcel IGCSE topic questions & solutions
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Interactive online lesson & practice
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Self-marking online worksheet
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Grade 5 topics
5A - Combining ratios5B - Direct and inverse proportion
5C - Reverse percentages5D - Standard form
5E - Speed5F - Changing the subject
5G - Quadratic expressions5H - Solving quadratic equations
5J - Drawing quadratic graphs5K - Cubic/reciprocal graphs
5L - Simultaneous equations5M - Sector areas and arc lengths
5N - Sim. equ. graphically5P - Midpoint of a line segment
5Q - Gradient of a line5R - Equation of a line
5S - Spheres and cones5T - Similar shapes (lengths)
5U - Trigonometry (SOHCAHTOA)5V - Exact trig. values
5W - Probability trees5X - Vectors
5Y - Venn diagrams5Z - Density
5AA - Pressure
GCSE Maths Grade 5 Revision Notes & Method

Guide to Sector areas and arc lengths: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

A sector with angle θ° at the centre is the fraction θ360 of a full circle of radius r: Arc Length = θ360 × 2πr and Area of Sector = θ360 × πr2.

Be careful when asked for the perimeter of a sector: the curved arc is only part of the boundary, so you must add the two straight radii as well (Perimeter = Arc Length + 2r).

Example 1: Find the area of a sector with radius 9 cm and angle 120°. Give your answer in terms of π and to 1 d.p.

Solution:

Area = 120360 × π × 92
= 13 × 81π = 27π cm2
Ans: 27π cm2 (84.8 cm2)
120° 9 cm

Example 2: Work out the total perimeter of a sector with radius 8 cm and angle 75° (to 1 d.p.).

Solution:

Arc = 75360 × 2π(8) = 10.47 cm
Add radii: 10.47 + 8 + 8
Answer: 26.5 cm (1 d.p.)
75° 8 cm 8 cm arc
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Sector areas and arc lengths Questions & Answers

Past Paper Example 1 AQA Jun 2024 1H Q12 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
A sector has radius 12 cm and angle 60°
60°12 cmNot drawnaccurately
Work out the length of the arc.
Give your answer in terms of π
Worked Solution & Mark Scheme (3 marks)
Arc length = (60 / 360) × 2 × π × 12 = 1/6 × 24π = 4π cm. M2 A1
Answer: Answer 4π cm
Past Paper Example 2 GCSE Nov 2022 1H Q15 3 marks
Full Paper (PDF) • Mark Scheme (PDF)
The diagram shows a sector of a circle of radius 18 cm.
x°18 cm18 cm
The length of the arc is 4π cm.
Work out the value of x.
Worked Solution & Mark Scheme (3 marks)
(x / 360) × 2 × π × 18 = 4π M1
⇒ (x / 10) = 4 M1
⇒ x = 40 A1
Answer: x = 40
Past Paper Example 3 GCSE May 2024 1H Q15 4 marks
Full Paper (PDF) • Mark Scheme (PDF)
OAB is a sector of a circle with centre O and radius 6 cm.
OAB6 cm6 cm
The length of the arc AB is 5π cm.
Work out, in terms of π, the area of the sector.
Give your answer in its simplest form.
Worked Solution & Mark Scheme (4 marks)
(The area of a sector is (angle ÷ 360°) × πr²)
Circumference = 2π(6) = 12π cm M2
Fraction of circle = 5π / 12π = 5/12 (angle = 150°) M1
Sector area = (5/12) × π × 6² = 15π cm². A1
Answer: 15π cm²

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