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MathidiaMathematics Academy
Circles and constructions
Lesson 51 of 75
Introduction

Circle calculations

Objective. Solve multi-step area and circumference problems.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Circle calculations develops a connected mathematical idea rather than an isolated trick. Reason with circle measures and accurate geometric constructions. Begin by representing the quantities or relationships, choose a rule that fits, justify each transformation, and finish by checking units, signs, scale and whether the answer is reasonable.

Worked example

Find the arc length of a 90° sector of radius 8 cm in terms of π.

Diagram of a circle
  1. 1Identify the known information, the unknown and any conditions.
  2. 2Choose a diagram, table, graph or algebraic representation that exposes the structure.
  3. 3Apply the relevant rule one justified step at a time, keeping exact values where useful.
  4. 4Check by substitution, inverse reasoning or estimation. The result is 4π cm.

Answer: 4π cm

Concept mastery

Based on your past attempts at this lesson — the question types to practise again come first.

Complete a practice set to see your concept breakdown here.

Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

Start practising

Common mistake. A common error in circle calculations is to copy a procedure without checking its conditions. Label the structure first and justify every sign, operation and unit.

Your progress

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