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Circle Formulae 1
The circumference
of a circle
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The circumference
of a circle
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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
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Summary
Circumference
= × Diameter
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Circle Formulae 2
The area of a circle
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or
If you click too soon you will miss the best bits.
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The area
of a circle
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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