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Circle Formulae 1

The circumference

of a circle

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or

If you click too soon you will miss the best bits.

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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