1 circle formulae 1 the circumference of a circle tandi clausen-may click the mouse
TRANSCRIPT
![Page 1: 1 Circle Formulae 1 The circumference of a circle Tandi Clausen-May Click the mouse](https://reader036.vdocuments.net/reader036/viewer/2022062519/5697bf871a28abf838c88fbe/html5/thumbnails/1.jpg)
1
Circle Formulae 1
The circumference
of a circle
Tandi Clausen-May Click the mouse
![Page 2: 1 Circle Formulae 1 The circumference of a circle Tandi Clausen-May Click the mouse](https://reader036.vdocuments.net/reader036/viewer/2022062519/5697bf871a28abf838c88fbe/html5/thumbnails/2.jpg)
2
Click the mouse only when you see
or
If you click too soon you will miss the best bits.
Click the mouse Click to see
Click the mouse
![Page 3: 1 Circle Formulae 1 The circumference of a circle Tandi Clausen-May Click the mouse](https://reader036.vdocuments.net/reader036/viewer/2022062519/5697bf871a28abf838c88fbe/html5/thumbnails/3.jpg)
3
The circumference
of a circle
Tandi Clausen-May Click the mouse
![Page 4: 1 Circle Formulae 1 The circumference of a circle Tandi Clausen-May Click the mouse](https://reader036.vdocuments.net/reader036/viewer/2022062519/5697bf871a28abf838c88fbe/html5/thumbnails/4.jpg)
4
First we need (pi)
Is it…..
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822172535…..?
What is ?Is it a number?
Click the mouse
![Page 5: 1 Circle Formulae 1 The circumference of a circle Tandi Clausen-May Click the mouse](https://reader036.vdocuments.net/reader036/viewer/2022062519/5697bf871a28abf838c88fbe/html5/thumbnails/5.jpg)
5
Well… not exactly.
is a ratio.
Click the mouse
![Page 6: 1 Circle Formulae 1 The circumference of a circle Tandi Clausen-May Click the mouse](https://reader036.vdocuments.net/reader036/viewer/2022062519/5697bf871a28abf838c88fbe/html5/thumbnails/6.jpg)
6
Pi is the number of times you must travel straight across the circle to go the same distance as all the way round the circle.
Once acrosstwice across
So is a bit more than 3.Click the mouse
Click to see the paths
three times acrossand a bit further!
![Page 7: 1 Circle Formulae 1 The circumference of a circle Tandi Clausen-May Click the mouse](https://reader036.vdocuments.net/reader036/viewer/2022062519/5697bf871a28abf838c88fbe/html5/thumbnails/7.jpg)
7
How can we be sure that
is a bit more than 3?
For a regular hexagon, the distance all the way round is exactly 3 times the distance straight across the middle.
123
Click the mouse
Click to see the paths
![Page 8: 1 Circle Formulae 1 The circumference of a circle Tandi Clausen-May Click the mouse](https://reader036.vdocuments.net/reader036/viewer/2022062519/5697bf871a28abf838c88fbe/html5/thumbnails/8.jpg)
8
And all the way round the circle is a little bit more than all the way round the hexagon.
So all the way round the circle is a little bit more than 3 times straight across the middle.
Circumference = × DiameterClick the mouse
Click to see the paths
![Page 9: 1 Circle Formulae 1 The circumference of a circle Tandi Clausen-May Click the mouse](https://reader036.vdocuments.net/reader036/viewer/2022062519/5697bf871a28abf838c88fbe/html5/thumbnails/9.jpg)
9Click the mouse
Summary
Circumference
= × Diameter
![Page 10: 1 Circle Formulae 1 The circumference of a circle Tandi Clausen-May Click the mouse](https://reader036.vdocuments.net/reader036/viewer/2022062519/5697bf871a28abf838c88fbe/html5/thumbnails/10.jpg)
10
Circle Formulae 2
The area of a circle
Tandi Clausen-May
Click the mouse
![Page 11: 1 Circle Formulae 1 The circumference of a circle Tandi Clausen-May Click the mouse](https://reader036.vdocuments.net/reader036/viewer/2022062519/5697bf871a28abf838c88fbe/html5/thumbnails/11.jpg)
11
Click the mouse only when you see
or
If you click too soon you will miss the best bits.
Click the mouse Click to see
Click the mouse
![Page 12: 1 Circle Formulae 1 The circumference of a circle Tandi Clausen-May Click the mouse](https://reader036.vdocuments.net/reader036/viewer/2022062519/5697bf871a28abf838c88fbe/html5/thumbnails/12.jpg)
12
The area
of a circle
Tandi Clausen-May Click the mouse
![Page 13: 1 Circle Formulae 1 The circumference of a circle Tandi Clausen-May Click the mouse](https://reader036.vdocuments.net/reader036/viewer/2022062519/5697bf871a28abf838c88fbe/html5/thumbnails/13.jpg)
13Click the mouse
We saw in Circle Formulae 1 that…
Circumference= × Diameter
Now, what about the area?
![Page 14: 1 Circle Formulae 1 The circumference of a circle Tandi Clausen-May Click the mouse](https://reader036.vdocuments.net/reader036/viewer/2022062519/5697bf871a28abf838c88fbe/html5/thumbnails/14.jpg)
14
Imagine a circle made out of strands of beads.
Open it out.
Click the mouseClick to see the circle open
![Page 15: 1 Circle Formulae 1 The circumference of a circle Tandi Clausen-May Click the mouse](https://reader036.vdocuments.net/reader036/viewer/2022062519/5697bf871a28abf838c88fbe/html5/thumbnails/15.jpg)
15
circumference
radius (half the diameter)
Let’s watch that again.
It’s a triangle!
base = circumference
Click to see the circle open again
height = radius (half the diameter)
Click the mouse
![Page 16: 1 Circle Formulae 1 The circumference of a circle Tandi Clausen-May Click the mouse](https://reader036.vdocuments.net/reader036/viewer/2022062519/5697bf871a28abf838c88fbe/html5/thumbnails/16.jpg)
16
circumference
radius (half the diameter)
= Circumference × Radius 2
Area of the triangle circle
Area of the triangle
We know how to find the area of a triangle.
Click the mouse
= Base × Height 2
![Page 17: 1 Circle Formulae 1 The circumference of a circle Tandi Clausen-May Click the mouse](https://reader036.vdocuments.net/reader036/viewer/2022062519/5697bf871a28abf838c88fbe/html5/thumbnails/17.jpg)
17
= Circumference × Radius 2
Area
Summary
Click the mouse
![Page 18: 1 Circle Formulae 1 The circumference of a circle Tandi Clausen-May Click the mouse](https://reader036.vdocuments.net/reader036/viewer/2022062519/5697bf871a28abf838c88fbe/html5/thumbnails/18.jpg)
18
Alternatively
![Page 19: 1 Circle Formulae 1 The circumference of a circle Tandi Clausen-May Click the mouse](https://reader036.vdocuments.net/reader036/viewer/2022062519/5697bf871a28abf838c88fbe/html5/thumbnails/19.jpg)
19
Area of a Circle
Split the circle into 8 equal sectors.
Arrange the sectors to resemble a shape that is roughly rectangular.
As the sectors get smaller and smaller the resulting shape eventually becomes a rectangle. The area of that rectangle is the same as the area of the circle.
½C
½C
r rA
A = ½ C x r
= ½ x 2 x π x r x r (C = 2 πr)= π x r x r= π r 2
![Page 20: 1 Circle Formulae 1 The circumference of a circle Tandi Clausen-May Click the mouse](https://reader036.vdocuments.net/reader036/viewer/2022062519/5697bf871a28abf838c88fbe/html5/thumbnails/20.jpg)
20
The End
Tandi Clausen-May