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.
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.)
ACMMG197: Investigate the relationship between features of circles, such as the circumference, radius and diameter; use formulas to solve problems involving circumference.