Volume and Surface Area

Students learn how to calculate the total surface area and volume of cuboids, prisms and convergent shapes.  Throughout the topic students develop their algebraic notation, and application of Pythagoras’ Theorem to aid their problem solving skills.  This topic takes place in Year 11 Term 2 for Foundation students and Year 10 Term 5 at higher level.

Volume and Surface Area Lessons

Prerequisite Knowledge

  • use standard units of measure and related concepts (length, area, volume/capacity
  • know and apply formulae to calculate: area of triangles, parallelograms, trapezia;
  • know the formulae: circumference of a circle = 2πr = πd, area of a circle = πr2; calculate: perimeters of 2D shapes, including circles; areas of circles and composite shapes

Success Criteria

  • know and apply formulae to calculate the volume of cuboids and other right prisms (including cylinders)
  • know the formulae to calculate the surface area and volume of spheres, pyramids, cones and composite solids

Key Concepts

  • To calculate the volume of a prism identify the cross-section and calculate its area. The volume is a product this area and its depth.
  • When calculating surface areas encourage students to illustrate their working by either writing the area on the faces of the 3D representation or create the net diagram so all individual faces can be seen.
  • While students are not necessarily required to derive the formulae for the volume and surface area of complex shapes they do need to be proficient with substituting in known values.

Common Misconceptions

  • Students often forget to include units when calculating volumes and areas.
  • It is important to differentiate between those which are prisms and those which are not. Encourage students to identify the cross-section whenever possible.


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