Stage 4 - space and geometry – 2D space
- Use a formula to find the circumference of a circle
- Identify that a fraction of a circle comprises a sector
- Calculate the perimeter of a figure
- Correctly round a calculation to a given unit
Activities to support the strategy
Students need to have confidence in using a formula to find the circumference of a circle, understand that sector is a fraction of a circle and have a well-developed understanding of perimeter. Review of each of these areas is encouraged before they are combined in more challenging perimeter problems.
1. Review the use of formula to find the circumference of a circle. Students need to apply either of the formulas below to calculate the circumference of a circle with confidence, given a particular radius or diameter. At this stage students should also have modelled concepts around rounding. It should be noted that π is an irrational number and answers can be given rounded to a given number of places or in exact form (in terms of π). Appropriate use of approximations of π and the calculator should also be discussed. Formulas and examples are shown below.
Calculate the circumference, given radius = 6 cm.
- Use π on your calculator and answer to 1 decimal place.
- ∴ Circumference is 18.8 cm (1 d.p.)
Calculate the circumference, given diameter = 10 m. Leave your answer in exact form
- ∴ Circumference is 10 π m
2. A number of examples demonstrating the perimeter of more complex figures involving circles and in particular the perimeter of a sector need to be presented. Students should also be given the opportunity to practice a variety of questions to build their understanding.
Calculate the perimeter.
- Take π=3.14 .
The perimeter of this figure is made up of a half-circle and the base. Using formula c=πd
- P=12 ×3.14×4+4
- ∴ Perimeter is 10.28 cm
Calculate the perimeter.
- Leave answer in terms of π
The perimeter of this figure is made up of a quarter-circle plus the two straight sides. Using formula c=2πr
- P=14 ×(2×π×3)+3+3
- P=3π2 +6
- ∴ Perimeter is (3π2 +6) cm
Calculate the perimeter. Use π on your calculator and answer correct to 2 decimal places
The perimeter of this figure is the two straight sides plus the curved fraction of the circle. Since there are 360° in a full revolution, the curved part of the perimeter is 50360 ×2πr
- P=(50360 ×2×π×4)+4+4
- ∴ Perimeter is 11.49 cm (2 d.p.)
Teachers should review the TIMES teacher guide on circles. A number of examples and teaching techniques are provided for measuring the perimeter of circles and more complex figures involving circles.
Students and teachers can review the activities provided on Supporting Australian Mathematics Project - Circles. The resource may be useful in helping students achieve that element of the year 8 achievement standards that refers to students naming the features of circles and calculating areas and circumferences of circles.
ACMMG197: Investigate the relationship between features of circles, such as the circumference, radius and diameter; use formulas to solve problems involving circumference
MA4-12MG: Calculates the perimeters of plane shapes and the circumferences of circles
- TIMES Module 17: Measurement and Geometry - the circle – teacher guide - In this module, the formulas for finding the circumference and area of a circle are introduced. The history and significance of the number pi is also included in this module.
- Supporting Australian mathematics project - Circles - designed for both teachers and students the website refers to the properties of circles including the circumference and area from the Australian Curriculum for year 8 students.