Where can I download free area and circumference PDF worksheets with answers?

On this MathsLinks page you can download free printable area and circumference PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, Ken Stafford (1), Maths Genie, Corbett Practice, Corbett Textbook, plus a printable one-page area and circumference revision guide.

What GCSE grade is area and circumference (3R)?

Area and circumference (topic code 3R) is a Grade 3 geometry topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Area and circumference Worksheets (PDF) with Answers — GCSE Maths

Free Area and circumference PDF Worksheets & Answers

Grade 3 • Topic 3R

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Ken Stafford (1) Practice worksheet & worked solutions	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Maths Made Easy MME worksheet & model answers	Qs	Ans
Dr Frost GCSE worksheet & solutions	Qs	Ans
Dr Austin (1) Practice grid / worksheet & answers	Qs	Ans
Dr Austin (2) Practice grid / worksheet & answers	Qs	Ans
Dr Austin (3) Practice grid / worksheet & answers	Qs	Ans
Dr Austin (4) Practice grid / worksheet & answers	Qs	Ans
Dr Frost (B. Blocks) Building Blocks skill sheet & answers	Qs	Ans
GCSE Maths Rocket Practice questions & answers	Qs	Ans
GCSE Maths Rocket (1) Practice questions & answers	Qs	Ans
1st Class Maths (Edxl) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (AQA) AQA exam questions & solutions	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
GCSE Maths Rocket (2) Practice questions & answers	Qs	Ans
E Classroom GCSE topic booklet & answers	Qs	Ans
PMT (Edxl) Edexcel GCSE topic questions & solutions	Qs	Ans
PMT (AQA) AQA GCSE topic questions & solutions	Qs	Ans
PMT (IGCSE) Edexcel IGCSE topic questions & solutions	Qs	Ans
Cognito Interactive online lesson & practice	Page
Circle parts Interactive online resource	Open
esheets Self-marking online worksheet	Page

Grade 3 topics
3A - Error intervals	3B - Operations with fractions
3C - Estimation	3D - Writing and simplifying ratio
3E - Ratio	3F - Proportion recipes
3G - Percentages	3H - Percentage change
3J - Exchange rates	3K - Conversions and units
3L - Scale drawings	3M - Best buy questions
3N - Substitution	3P - Solving linear equations
3Q - Straight line graphs	3R - Area and circumference
3S - Rotations	3T - Reflections
3U - Enlargements	3V - Translations
3W - Mixed transformations	3X - Area of compound shapes
3Y - Frequency trees	3Z - Two way tables

Explanation:

For any circle with radius r and diameter d = 2r: the Circumference (perimeter) is C = πd (or 2πr), and the Area is A = πr². Always check whether the question gives you the radius or the diameter before starting!

If the question asks for your answer in terms of π (non-calculator), leave π as a symbol in your answer (e.g. 25π cm²). Remember that the perimeter of a semicircle includes the straight diameter as well as the curved arc: Perimeter = 12πd + d.

Example 1: A circle has a diameter of 12 cm. Work out its area and circumference to 1 d.p.

r = 12 ÷ 2 = 6 cm

A = π × 6² = 113.1 cm²

C = π × 12 = 37.7 cm

Example 2: Work out the perimeter of a semicircle with radius 5 cm. Give your answer to 1 d.p.

d = 2 × 5 = 10 cm

Arc = 12π(10) = 15.71 cm

15.71 + 10 = 25.7 cm

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Area and circumference Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 GCSE May 2018 1F Q9 2 marks

Full Paper (PDF) • Mark Scheme (PDF)

The centre of this circle is marked with a cross (×).

(a) Write down the mathematical name of the straight line shown in the circle. [1 mark]

(b) Write down the mathematical name of the straight line that is touching the circle. [1 mark]

Worked Solution & Mark Scheme (2 marks)

Part (a) Solution:

Line from centre to circumference is a radius B1

Answer (a): Radius

Part (b) Solution:

Line touching circle at one point is a tangent B1

Answer (b): Tangent

Past Paper Example 2 OCR Jun 2025 3F Q1 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

The diagram shows a circle, centre O, and a straight line.

(a) the straight line [1 mark]

the perimeter of the circle. [1 mark]

(b) On the diagram, draw a diameter. [1 mark]

Worked Solution & Mark Scheme (3 marks)

Part (a) Solution:

A straight line joining two points on the circumference is a chord. B1

Answer (a): Chord

Part Solution:

The perimeter of a circle is called the circumference. B1

Answer : Circumference

Part (b) Solution:

Draw a straight line passing through O from one side of the circumference to the other. B1

Answer (b): Straight line drawn through centre O joining two points on the circumference

Past Paper Example 3 IGCSE Nov 2023 1F Q19 / 1H Q5 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

The diagram shows a shaded shape made from three identical semicircles, X, Y and Z.

ABCDE is a straight line.
AC is the diameter of semicircle X and B is the centre of semicircle X
BD is the diameter of semicircle Y and C is the centre of semicircle Y
CE is the diameter of semicircle Z and D is the centre of semicircle Z
AC = BD = CE = 20 cm
Work out the perimeter of the shaded shape.
Give your answer correct to the nearest whole number.

Worked Solution & Mark Scheme (3 marks)

Each semicircle arc = ½ × π × 20 = 10π ≈ 31.416 cm M1
Straight segments AB = 10 cm and DE = 10 cm M1
Perimeter = 3 × 10π + 10 + 10 = 30π + 20 = 114.247... ≈ 114 cm. A1

Answer: 114 cm

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Area and circumference

Free Area and circumference PDF Worksheets & Answers

Guide to Area and circumference: Explanation, Diagrams & Worked Examples

GCSE Past Paper Area and circumference Questions & Answers