Circles, Cylinders and Circular Shapes

Circles, cylinders and circular shapes follows on from area of 2D shapes and surface area of 3D cuboids and prisms which students study in Term 2 of Year 8.  In this unit students learn how to calculate the circumference and area of circles both as decimals and in terms of π.  Learning progresses from 2D circles to finding the total surface area and volume of cylinders.  Circles, cylinders and circular shapes typically takes  6 one hour lessons.


Circles, Cylinders and Circular Shapes  Lessons
Circumference of a Circle

Problems with Circular Shapes

Surface Area of a Cylinder

Volume of a Cylinder



Prerequisite Knowledge
  • Derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms
  • Calculate and solve problems involving: perimeters of 2-D shapes and composite shapes.

Key Concepts
  • The radius is the distance from the centre to any point on the circumference.  The plural of radius is radii.
  • The diameter is the distance across the circle through the centre.
  • π is a Greek letter used to represent the value of the circumference of a circle divided by its diameter.
  • The circumference is the distance about the edge of a circle. The circumference of a circle can be calculated as:
    • C = πD where D is the diameter, or,
    • C = 2πr where r is the radius.
  • The area of a circle can be calculated using the formula
    • A = πr2 where r is the radius.
  • A cylinder is a circular prism.


Working mathematically

Develop fluency

  • Use language and properties precisely to analyse numbers, algebraic expressions, 2-D
    and 3-D shapes, probability and statistics.
  • Use algebra to generalise the structure of arithmetic, including to formulate
    mathematical relationships
  • Substitute values in expressions, rearrange and simplify expressions, and solve
    equations

Reason mathematically

  • Make and test conjectures about patterns and relationships; look for proofs or counterexamples
  • Begin to reason deductively in geometry, number and algebra, including using geometrical constructions

Solve problems

  • Begin to model situations mathematically and express the results using a range of
    formal mathematical representations
  • Select appropriate concepts, methods and techniques to apply to unfamiliar and nonroutine
    problems.

Circles, Cylinders and Circular Shapes Subject Content

Shape

  • Derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies
  • Calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes
  • Derive and apply formulae to calculate and solve problems involving: perimeter and area of  circles and cylinders.

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