pi day by Simon Pampena Working out the Area of a Circle Calculating pi 1 The formula for the area inside a circle is area = radius x radius x But why? Let’s see if we can make sense of this formula. In this activity we will: 1. Understand how the circle area formula works. 2. See who can work out the best approximation of pi using real circles. radius 2 Materials Needed 1. A4 single sided paper 2. Compass or largish circular object to trace 3. Scissors 4. Ruler 5. Pencil 6. Sticky tape 3 Step 1. Draw as perfect a circle as you can. Make sure it is at least 20cm in diameter... that’s a 10cm radius. A compass is preferred but feel free to try other methods. 4 Step 2. Next, fold your circle in half trying to be as precise as possible. This is all about perfection! 5 Step 3. Cut along your fold line until you have two identical semicircles. 6 Step 3. Now fold each semicircle in half, again being as precise as possible, and cut along your new fold lines. 7 Step 4. Repeat the process for your quarters, folding them in half, and cutting along the new fold lines. 8 Step 5. Finally, take one of the eighths and fold that one in half and make one last cut along the fold line. 9 Step 6. Now sticky-tape together all your wedges like a puzzle so you end up making a rectangular shape. 10 Step 7. With your ruler you can now measure out the length and the height of the bumpy rectangle. height length 11 Step 8. Multiply the height by the length and see what you get. Next multiply the height by the height by pi and see what you get. What difference is there? Why? height ! length = ? height ! height ! = ? 12 height height 13 length length length 14 height length height = radius = ish length height 15 For your puzzle work out length height How close to pi did you get? How can you get more ?! 16 Step 9. Fold and cut your rectangle into halves, then each half into quarters, then each quarter into eighths. 17 Step 10. Now rearrange your pieces so you can stick together all your wedges again making another rectangular shape. 18 Step 11. With your ruler re-measure the length and the height of the less bumpy rectangle. Then work out length over height. length height height length 19 Who got the most... in your group? 20 Teacher’s Notes Page 4 To make cutting easier, circles need to be around 20 cm in diameter. Pages 5 - 9 Precision is important. Make sure everyone’s folds and cuts are as accurate as possible. Page 12 When calculating with pi use 3.14 Pages 13 Illustration of the relationship between the area of the rectangle and the circle area formula. Pages 14 - 15 Illustration of the connection between the height, length and pi ish i.e. an approximation of pi . Pages 17 - 19 After folding and cutting the rectangle into smaller sections the approximation of pi should improve. 21