# pi day by Simon Pampena Working out the Area of a Circle Calculating

```pi day
by Simon Pampena
Working out the Area of a Circle
Calculating pi
1
The formula for the area inside a circle is
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.
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
=
=
ish
length
height
15
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...
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
```