# Mathematics / Year 9 / Measurement and Geometry / Using units of measurement

Curriculum content descriptions

Calculate the surface area and volume of cylinders and solve related problems (ACMMG217)

Elaborations
• analysing nets of cylinders to establish formulas for surface area
• connecting the volume and capacity of a cylinder to solve authentic problems
General capabilities
• Literacy Literacy
• Numeracy Numeracy
• Critical and creative thinking Critical and creative thinking
ScOT terms

Volume (Dimensions),  Cylinders,  Surface area

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Year level 9-10
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Learning area Mathematics

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### 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.

### 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.

### Volume of prisms and cylinders?

You may know how to work out the volume of a rectangular prism: just use the formula V = length x width x height. Easy! But what about the volume of a cylinder? See how to calculate it, and notice that the formula includes the area of a circle and one other dimension.

### Is it a prism? What's its volume?

What makes a prism a prism? Here's a clue: it has to do with its cross-section. See how to work out the volume of different prisms.

### Surface area and volume of prisms and cylinders

This is a website designed for both teachers and students, which addresses the surface area and volume of prisms and cylinders from the Australian Curriculum for year 9 students. It contains material on calculating the surface area and volume of prisms and cylinders. There are pages for both teachers and students. The student ...

### Volume of a cylinder

How do you work out the volume of a cylinder? Watch how it's done and discover why knowing how to work out the area of a circle helps. Try a problem that involves finding the diameter of half a cylinder.

### Total surface area of a cylinder

The total surface area of a cylinder is the sum area of the two circular ends and the curved surface area. There's a trick to working out the curved surface area of a cylinder. See how it helps you work out the total surface area of a cylinder. Watch what to do when there is only quarter of a cylinder.

### Measures: volumes

Compare the volumes of a range of rectangular prisms when scaling up (enlarging) side lengths by different ratios. Notice that the rectangular prisms are not similar in the mathematical sense, but it is possible to predict the effect on the volume produced by the scaling of the sides. Identify and describe the relationship ...

### Measures: scaling up solids

Compare the volumes of cubes and rectangular prisms before and after being scaled up (enlarged). Notice that 'similar solids' in the mathematical sense have the same shape but different volumes. Explore the relationship between side length and volume when scaling up solids. This learning object is the fifth in a series ...

### Measures: scaling down solids

Compare the volumes of cubes and rectangular prisms before and after being scaled down (reduced). Notice that 'similar solids' in the mathematical sense have the same shape but different volumes. Explore the relationship between side length and volume when scaling down solids. This learning object is the sixth in a series ...

### BBC Bitesize: volume - revision

This is a set of information sheets on measurement ideas associated with volumes of rectangular prisms and cylinders. Practice and test questions with answers are provided. This resource is one of a series of online resources from the BBC's Bitesize collection.

### Surface area of prisms

This is a five-page HTML resource about solving problems concerning surface areas of prisms. It contains one video and five questions, two of which are interactive. The resource discusses and explains solving problems involving determining surface areas of prisms to reinforce students' understanding.

### Working it out!

See how small a cubic centimetre looks when compared with a cubic metre (100 cm x 100 cm x 100 cm). Then estimate the volume of cuboids, such as a packet of food and a tool box. Rotate a 3D grid to help you work out dimensions in centimetres. First work out the area of the base. Then multiply your answer by the height to ...

### 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.

### Measures: scaling surface area

Compare the surface area of cubes and rectangular prisms before and after being scaled up (enlarged) or scaled down (reduced). Notice that 'similar shapes' in the mathematical sense have the same shape but different surface areas. Explore the relationship between side length and surface area when scaling solids. This learning ...

### 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 ...

### 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 ...

### 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.

### Starting Smart: how can I use measurement relationships to solve problems? - years 7-9

This curriculum resource package is a ten-week middle years teaching plan and set of supporting resources to extend students' knowledge and skills in the measurement of area and volume and to develop their ability to solve practical measurement problems. Students use counting methods and develop formulas to calculate areas ...

### TIMES Module 11: Measurement and Geometry: area, volume and surface area - teacher guide

This is a 15-page guide for teachers containing explanations of the derivation of formulas for the areas of parallelograms, trapeziums, rhombuses and kites. Formulas for the volumes and surface areas of prisms and cylinders are obtained. Applications of these formulas are given. A history of the development of these concepts ...