Lesson Notes By Weeks and Term v5 - Grade 11

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Calculate surface area and volume of composite 3D objects.
• Apply trigonometry to find unknown dimensions.
• Solve practical problems involving surface area and volume.
• Convert between different units of measurement.

Lesson summary

This week, we delve deeper into Measurement, focusing on applying area and volume calculations to more complex shapes and problem-solving scenarios. Measurement is a crucial skill, not just in Mathematics, but in everyday life. From calculating the amount of paint needed for a room to determining the volume of water in a swimming pool, or even understanding land sizes, measurement is essential for informed decision-making. This week, we’ll concentrate on combining different geometric shapes and using our knowledge of trigonometry to calculate areas and volumes. This builds upon the Grade 10 Measurement concepts, which focused on simpler shapes.

Lesson notes

This week's focus is on extending our Grade 10 knowledge of area and volume to more complex shapes and applications. We’ll look at composite shapes, incorporating trigonometry to find missing dimensions, and solving real-world problems.

Composite 3D Objects: These are objects formed by combining two or more basic geometric shapes (e.g., a cylinder with a cone on top). To find the surface area of a composite object, you need to carefully consider which surfaces are exposed and which are joined together. To find the volume, you simply add the volumes of the individual components.

Using Trigonometry: Trigonometry is frequently needed to find missing dimensions (e.g., height, slant height, radius) in area and volume calculations, especially when dealing with cones, pyramids, and prisms with triangular faces.

Remember SOH CAH TOA: sin θ = Opposite / Hypotenuse cos θ = Adjacent / Hypotenuse tan θ = Opposite / Adjacent Unit Conversions: Proficiency in unit conversions is essential. Here’s a reminder of common conversions: 1 m = 100 cm = 1000 mm 1 km = 1000 m 1 litre (L) = 1000 millilitres (ml) = 1000 cm³ 1 m³ = 1000 litres (L) 1 kg = 1000 g 1 tonne = 1000 kg Formulas to Remember (supplied on the formula sheet, but you must know how to use them!)

Area of a rectangle: `l x b` Area of a triangle: `½ x b x h` Area of a circle: `πr²` Curved surface area of a cylinder: `2πrh` Surface area of a sphere: `4πr²` Volume of a prism/cylinder: `Area of base x height` Volume of a pyramid/cone: `⅓ x Area of base x height` Volume of a sphere: `(4/3)πr³`

Worked example

Example 1: Composite Object – Silo

A grain silo consists of a cylinder with a hemisphere on top. The cylinder has a diameter of 8 meters and a height of 12 meters.

a) Calculate the volume of the silo.

b) Calculate the total surface area of the silo (including the base).