Volume and Surface Area

August 23, 2016

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 Lesson

Volume of Prisms

Surface Area of Prisms

Volume and Surface Area Investigation

Total Surface Area and Volume Investigation

Metric Conversions of Volume and Area

Cylinders

Spheres

Surface Area of Square Based Pyramids

Pyramids

Volume of a Cone

Surface Area of a Cone

Revision Lessons

Volume and Surface Area of Cuboids

Volume of Prisms

Spheres, Cones and Pyramids

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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