Mathematics / Year 10 / Measurement and Geometry / Using units of measurement

View on Australian Curriculum website Australian Curriculum, Assessment and Reporting Authority
Curriculum content descriptions

Solve problems involving surface area and volume for a range of prisms, cylinders and composite solids (ACMMG242)

Elaborations
  • investigating and determining the volumes and surface areas of composite solids by considering the individual solids from which they are constructed
General capabilities
  • Literacy Literacy
  • Numeracy Numeracy
ScOT terms

Volume (Dimensions),  Cylinders,  Prisms,  Surface area

Teacher resource

Secondary mathematics: using real data

These seven learning activities, which focus on the use of 'real data' using a variety of tools (software) and devices (hardware), illustrate the ways in which content, pedagogy and technology can be successfully and effectively integrated in order to promote learning. In the activities, teachers use the three content strands ...

Interactive resource

EagleCat: scale it

Explore changes in area when a shape is acted on by a scale factor. Examine changes in volume when an object is acted on by a scale factor. Analyse the changes using whole numbers.

Teacher resource

Turn up the volume - unit of work

In this unit of work students explore and explain the connections between the surface area and volume of different shapes and how each attribute is measured.

Interactive Resource

Laptop wrap: Under the surface

In this laptop-friendly resource, students consider the difference between volume and surface area before posing practical problems. They then consider issues relating to unit conversions and similar figures.

Text

In a spin

This resource is a web page containing a short task to explore volume of a solid shape. The task involves calculating the volume of the solid formed by rotating a right angled triangle about its hypotenuse A printable resource and solution is also available to support the task. This resource is an activity from the NRICH website.

Video

Volume of a cone

In this learning object the relationship between the volume of a cylinder and cone is illustrated. Problems with animated worked solutions are included as are practice questions and answers for students.

Text

Volume of a Pyramid and a Cone

This resource is a web page containing an investigative task to explore volume. Derive the formulae for the volumes of a square-based pyramid and a cone, using mathematical concepts. A printable resource is also available to support the task. This resource is an activity from the NRICH website.

Moving Image

Surface area of a sphere

What's the formula for finding out the surface area of a sphere? See how to apply the formula in a couple of examples. Watch how to give the answer in decimals or in terms of pi. How do you find the surface area of half a sphere? Check out the example.

Teacher resource

Secondary mathematics: different representations

These seven learning activities, which focus on 'representations' using a variety of tools (software) and devices (hardware), illustrate the ways in which content, pedagogy and technology can be successfully and effectively integrated in order to promote learning. In the activities, teachers use different representations ...

Teacher resource

Delivering water

This is a mathematics unit of work about water: its world-wide availability and use; the time spent carrying it; the best shape for water tanks; and the area of land taken up around tanks and in paths and ditches to water sources. Intended for years 9 and 10 and written from a global education perspective, the resource ...

Moving Image

Volume of pyramids and cones

A typical pyramid has a square base, but a cone is a pyramid with a circular base. See how to use a third of the base area to work out the volume of a pyramid or a cone. Can you guess what other dimension is needed?

Moving Image

Ancient Egyptians knew the volume of a pyramid

An ancient text called the Moscow Papyrus, written some 4000 years ago, reveals that ancient Egyptians worked out the formula for calculating the volume of a pyramid. See how they derived this formula based on the volume of a cube.

Teacher resource

TIMES Module 12: Measurement and Geometry: cones, pyramids and spheres - teacher guide

This is a 26-page guide for teachers. It contains an introduction to finding the surface area and volume of cones, cylinders, pyramids and spheres.

Moving Image

Volume of a sphere

What's the formula to find out the volume of a sphere? See how to apply the formula in a couple of examples. In the second, the answer is to be found in terms of pi. What effect does the length of radius have on a sphere's volume?

Moving Image

What's a frustum and can you work out its volume?

Imagine a pyramid or a cone with its apex removed. The remaining shape is called a frustum. Are you up to the challenge of working out the volume of one of these shapes? There are a few steps involved, but we'll take you through them.

Moving Image

Circular-based pyramids?

Did you know that a cone is a circular-based pyramid? Find out how to work out the surface area of a cone and of a typical square-based pyramid. See how slant height is used in working out the total surface area of a cone.