Circles, Cylinders and Circular Shapes

Circumference of a Circle

Area of a Circle

Problems with Circular Shapes

Total 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.