## Activity Introduction

Quick summary: Students use Pi to calculate the area and volume of aluminium cans. They compare a range of methods to estimate the value of Pi.

This lesson has been developed as part of the Schools Recycle Right Challenge for Planet Ark’s National Recycling Week. Register your lesson or other activities so they can be counted towards the national achievement and to receive other free support materials.

Learning goals for this activity include:

• Students analyse cylinders to establish formulas for surface area.
• Students solve authentic problems.

Australian Curriculum content descriptions:

Year 9 Mathematics:

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

Time needed: 50 min

Level of teacher scaffolding: Medium – encourage students to think outside the ‘square’ when trying to come up with creative solutions for circles.

Resources needed: Washed aluminium cans, rulers, callipers, accurate measuring jugs or weighing scales, string, protractors and any other equipment students might wish to try to solve their problems

Digital technology opportunities: Calculators, digital weighing equipment.

There’s an app for that: Pi - Fastest Pi(π) computation/benchmark program.

Assumed prior learning:  Used compass, draw circles, measure length accurately, understands the concept of approximation, used different units of volume and weight, has used volume measuring flasks/cups.

Key words: Circumference, diameter, radius, Pi, irrational number, volume, area.

Cool Australia’s curriculum team continually reviews and refines our resources to be in line with changes to the Australian Curriculum.

These Planet Ark resources were developed by Cool Australia with funding from the Alcoa Foundation.

## Worksheets

### Teacher preparation

Overarching learning goals: Explore the constant Pi by solving problems and using various methods for measuring.

Teacher content information:

Students will be using aluminium cans to investigate Pi in this activity. Aluminium can be continually recycled. It only takes 5% of the energy to recycle a can compared to making it from raw materials.

The aluminium can is pressed to maximise its strength while using only enough aluminium to successfully fulfil its purpose. It must be able to be dropped without breaking while also containing the internal pressure and prevent leaks. It needs to be easy to open and safe to drink from the can. Aluminium has the advantage of being easy and quicker to chill compared with other materials. These properties of aluminium make it a particularly good packaging material.

Pi is a mathematical constant. Pi is represented by this symbol π.  It is the ratio of a circle’s circumference to its diameter. Pi is an irrational number so the

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### Thought Starter: Find 3 things around you that are ciruclar...

Step 1: It’s in the can

1. Describe the main surfaces of an aluminium can:

These formulas and information may be of use:

 The symbol used for Pi is π Estimation of Pi as a fraction 22/7 Estimation of Pi to 5 decimal places 3.14159 Calculating circumference Pi * Diameter π *d Calculating area of a circle Pi * radius2 π *r2 Calculating volume of a cylinder Pi * radius2 * height π *r2*h Relationship between volume and weight of water 1gm = 1cc

Step 2: Start calculating

2. How much aluminium is in a can? Make measurements of the can using equipment of your choice.

Diameter of can

Height of can

Area of the top and bottom of the can

Area of the side of the can

The total area of the can

3. What is the volume of a can? Consider the height you measured for the area of aluminium. Both the tops and bottom of the can are

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