Student worksheet

Thought-Starter: Find 3 things around you that are circular...

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 r²h
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 indented. What is a better approximation of the height?

New estimated height

Calculated volume of the can

Does you calculation match the volume on the label?

Step 3

What’s that constant?

You will try more than one method to estimate Pi. Your challenge will be to find which method provides the best accuracy. Four examples of measuring Pi are provided. You can also invent your own methods. You will need to make measurements and then us them in the correct formula to find the answer for Pi.

Measuring the circumference: Use a string or tape, wrap it around the can and measure the length. You will need an accurate measurement of the diameter.

Measure the area of aluminium: Mark the can. Roll the can along a ruler until it has gone a full circle. Take the measurement from the ruler. You will need an accurate measurement of the diameter.

Measure the volume in a cylinder: Measure the (internal) height and diameter of an aluminium can. Weigh or measure the volume of the amount of water it takes to fill the can. You will need an accurate measurement of the diameter and internal height of the can.

Using geometry: This will not need a can. Draw a large circle. Draw an accurate 5 degree segment. Measure the end of the triangle. By multiplying this length by 72 you will have an approximate circumference. If your equipment is accurate enough try doing the same with a 2 degree segment and multiplying by 180.

Method 1

Formula used

Calculation of Pi

Method 2

Formula used

Calculation of Pi

Method 3

Formula used

Calculation of Pi

Method 4

Formula used

Calculation of Pi

Which method did you find was the most accurate?

National Recycling Week - Time for Pi

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