NSW Syllabuses

Mathematics K–10 - Stage 5.2 - Measurement and Geometry Area and Surface Area

Outcomes

A student:

• MA5.2-1WM

selects appropriate notations and conventions to communicate mathematical ideas and solutions

• MA5.2-2WM

interprets mathematical or real-life situations, systematically applying appropriate strategies to solve problems

• MA5.2-11MG

calculates the surface areas of right prisms, cylinders and related composite solids

Related Life Skills outcome: MALS-29MG

Content

• Students:
• Calculate the surface areas of cylinders and solve related problems (ACMMG217)
• recognise the curved surface of a cylinder as a rectangle and so calculate the area of the curved surface
• develop and use the formula to find the surface areas of closed right cylinders:
$$\mbox{Surface area of (closed) cylinder} = 2\pi r^2 + 2 \pi r h$$ where $$r$$ is the length of the radius and $$h$$ is the perpendicular height
• solve a variety of practical problems involving the surface areas of cylinders, eg find the area of the label on a cylindrical can
• interpret the given conditions of a problem to determine whether a particular cylinder is closed or open (one end only or both ends) (Problem Solving)
• Solve problems involving surface area for a range of prisms, cylinders and composite solids (ACMMG242)
• find the surface areas of composite solids involving right prisms and cylinders
• solve a variety of practical problems related to surface areas of prisms, cylinders and related composite solids, eg compare the amount of packaging material needed for different objects
• interpret the given conditions of a problem to determine the number of surfaces required in the calculation (Problem Solving)

Language

Students are expected to be able to determine whether the prisms and cylinders referred to in practical problems are closed or open (one end only or both ends), depending on the context. For example, objects referred to as 'hollow cylinders' or 'pipes' represent cylinders that are open at both ends.