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Circle Formulae 1
The circumference
of a circle
Tandi Clausen-May Click the mouse
2
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or
If you click too soon you will miss the best bits.
Click the mouse Click to see
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3
The circumference
of a circle
Tandi Clausen-May Click the mouse
4
First we need (pi)
Is it…..
3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822172535…..?
What is ?Is it a number?
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Well… not exactly.
is a ratio.
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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
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three times acrossand a bit further!
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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.
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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
9Click the mouse
Summary
Circumference
= × Diameter
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Circle Formulae 2
The area of a circle
Tandi Clausen-May
Click the mouse
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
12
The area
of a circle
Tandi Clausen-May Click the mouse
13Click the mouse
We saw in Circle Formulae 1 that…
Circumference= × Diameter
Now, what about the area?
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Imagine a circle made out of strands of beads.
Open it out.
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circumference
radius (half the diameter)
Let’s watch that again.
It’s a triangle!
base = circumference
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height = radius (half the diameter)
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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.
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= Base × Height 2
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= Circumference × Radius 2
Area
Summary
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Alternatively
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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
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The End
Tandi Clausen-May
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