Primary 6 · Chapter 6
Find circle areas and circumferences, then combine curves and shapes in composite figures.
Self-paced lessons · Modelled on top school exam questions · No sign-up for the samples
The Circle chapter
Watch · The introduction
Roll out the circle's edge
Begin with circumference, then use radius, diameter and arcs to build circle area and composite figures.
Try · Modelled on top school exam questions
Try each question yourself first, then check your answer or compare it with the solution. These questions are written by Mathweave, not copied from school papers. No sign-up is needed.
Question 1 of 3
Choose diameter or radius carefully before using the circumference formula.
A round clock face has a diameter of 18 cm. Find the circumference of the clock face. (Take π = 3.14.)
Ans: 56.52 cm
Question 2 of 3
Halve the diameter to get the radius before finding the area.
A round cake board has a diameter of 20 cm. Find the area of the board. (Take π = 3.14.)
Ans: 314 cm²
Question 3 of 3
Break the path into the circular and straight regions shown in the figure.
A garden path of width 2 m throughout turns a right-angled corner. One straight arm of the path is 8 m long, the other is 6 m long, and the bend at the corner is a quarter ring with an inner radius of 4 m. Find the total area of the path. (Take π = 3.14.)
Ans: 43.7 m²
Follow a lesson link beside a question, or browse the chapter below.
The chapter · Nine question types
A linked row opens a published lesson with its own film. Explore the explanation and available practice on that page.
The order · Four groups
Circumference and area of a whole circle
6.1 and 6.2
Semicircles, quarter circles and composite figures
6.3 to 6.5
Reading the figure: which length, and which quantity
6.6 and 6.7
The top tier
6.8 and 6.9
These harder types recover a length from nested shapes or compare overlapping regions without finding their shared part.
The number tells you where a question type sits in this chapter, not what your child needs to learn first. A child who has already met a type in school can practise it without working through the ones above it.
The papers · Modelled against top school papers
Paper 1 has 30 questions for 50 marks: 18 multiple-choice questions and 12 short-answer questions. Paper 2 has 15 questions for 50 marks: 5 short-answer questions and 10 structured or long-answer questions.
A Paper 1 question is usually one circle on its own, a circumference or an area, and it is where an answer is most often left in terms of π. The three- and four-mark items appear in Paper 2, and there the figure is made of more than one shape, or one of the lengths the rule needs has been left off it.
Close to half of Paper 2 questions combine two or more topics. A longer question may use a circle for only one arc or area. Practice questions are not labelled by type, so children must choose the methods they need.
Everything here is modelled against top school papers. Those papers are never reproduced, and every question on this site is original.
Written working · Clear methods, line by line
These examples show Mathweave's clear, consistent layout for each method. The layout is informed by the answer keys we reviewed.
Parents · Asked and answered
The question types follow the latest MOE Primary Mathematics syllabus. The syllabus defines what is taught; the papers we model against show how it is examined.
Whichever one the question prints, and a question that evaluates π prints one. The choice belongs to the setter: any length entering the π step that is not a multiple of 7 forces 3.14. Where a question gives no value at all, it wants the answer left in terms of π.
We write the questions ourselves rather than copy them from papers. Each chapter is modelled on the types of question that top school papers set. A question may look like one your child has met before because it is the same type.
Practice uses different numbers for each question type, points out the common mistake when your child makes it and records which types your child can complete independently.