logo

Learning objective

Perform calculations related to the circumference and area of a circle, where answers may be expressed in terms of π. Additionally, calculate the arc length and sector area as fractions of the circle's circumference and area, including both minor and major sectors.

Read the explanation, check the common trap, then practise with flashcards and questions.

Practise this topicRead the exam answerTopic hub

Exam focus

  • Read the explanation.
  • Check key terms.
  • Practise with linked questions.
Cambridge IGCSE MathematicsExtended MensurationSupplement content

Study support

Understand this objective

Quick explanation

Perform calculations related to the circumference and area of a circle, where answers may be expressed in terms of π. Additionally, calculate the arc length and sector area as fractions of the circle's circumference and area, including both minor and major sectors

  • This point belongs to Circles, arcs and sectors, especially Circles, arcs and sectors outcomes.
  • You need to be able to perform calculations related to the circumference and area of a circle, where answers may be expressed in terms of π. Additionally, calculate the arc length and sector area as fractions of the circle's circumference and area, including both minor and major sectors.
  • The key ideas to know are Calculate, Determine, and Show.
  • Use the linked flashcards and practice questions to check recall, then practise applying the idea in an exam-style answer.

Key concepts

CalculateDetermineShowWork out

Why it matters

This objective helps connect Circles, arcs and sectors outcomes to exam-style questions, flashcards, and revision notes for Circles, arcs and sectors.

Revision tools

Choose how to practise

Back to topic hub
Flashcards10 linked cards

Flashcard 1 of 10

Press Space to flip, arrows to move
Practice Questions7 linked questions

Question 1 of 7

Choose an answer, get feedback, then move sideways through the set.

0 of 5 attempted

Paper 2 structured question: Circles, arcs and sectors

Paper 2Core or Extended Mathematics6 marks

Diagram Description

Circle with radius 7 cm and central angle 60°

A circle has radius 7 cm. A sector of the circle has a central angle of 60°. Calculate the circumference, area, arc length of the sector, and the area of the sector. Express all answers in terms of π where appropriate.

QuantityFormulaCalculationAnswer
Circumference2πr2 × π × 714π cm
Areaπr²π × 7²49π cm²
Arc length(θ/360) × 2πr(60/360) × 2 × π × 7(1/6) × 14π = 14π/6 = 7π/3 cm
Sector area(θ/360) × πr²(60/360) × π × 7²(1/6) × 49π = 49π/6 cm²
  1. a

    Calculate the circumference of the circle in terms of π.

    Aim for approximately 1 distinct marking point.

    [1]
  2. b

    Calculate the area of the circle in terms of π.

    Aim for approximately 1 distinct marking point.

    [1]
  3. c

    Calculate the length of the arc corresponding to the 60° sector, in terms of π.

    Aim for approximately 2 distinct marking points.

    [2]
  4. d

    Calculate the area of the sector with central angle 60°, in terms of π.

    Aim for approximately 2 distinct marking points.

    [2]
Revision notestopic notes

Open the full topic revision notes when you are ready to review this objective in context.

Open revision notes

Related learning objectives

No linked resources are published for this section yet.

Revision hubs

Move back to a broader study route

Cambridge IGCSEMathematics resources