Circles

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Circles
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What is a circle?
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Well, a circle is a circular object that is..
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Wait a minute!
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A circle is this round object that...
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Wait a minute!
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This isnt as easy as I thought it was going to
be.
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A circle is a bunch of points that are all the
same distance away from a starting point.
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Suppose that this is our starting point.
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Now lets consider a point that is 5 inches away
from our starting point.
5 inches
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Now lets consider another point that is 5 inches
away from our starting point.
5 inches
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And another point!
5 inches
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And another point!
5 inches
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And another point!
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And another point!
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And another point!
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And another point!
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And so on!
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Now were starting to see a circle.
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Pretty soon, this collection of points makes a
circle.
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This circle has a radius of 5 inches because each
point on the circle is 5 inches away from our
starting point.
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You can think of a radius as a bicycle spoke.
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If the length of the radius is doubled, then you
have a diameter.
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The diameter cuts the circle into two halves.
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The perimeter of a circle has a special name.
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A circles perimeter is called the circumference.
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How in the world would you find the circumference
of a circle?
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You could take a piece of string and measure
the circumference using the string.
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Then measure the length of the string.
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There is, however, a more mathematical way of
calculating the circumference.
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EVERY circle has a certain property to it.
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It takes 3.14 diameters to make the circumference
of any circle.
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Lets take a closer look.
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3.14 diameters
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PRESTO!
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This property is true for ANY size circle.
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This number, 3.14, has a special name. It is
called pi.
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Pi is not a recent discovery. It is thought that
pi was discovered by the Greek mathematician
Hippocrates around 430 B.C.
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Pi is simply a number that can help you find the
circumference of any circle as long as you know
the length of the diameter.
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This is the symbol for pi.
?
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For example, here is a circle with a diameter of
10 cm.
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That means that you can take 3 diameters of 10 cm
plus a little extra and wrap it around the
circle.
10 cm
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So the circumference 3.14 x 10 31.4 cm.
10 cm
10 cm
10 cm
10 cm
1.4 cm
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Here is a circle with a diameter of 20 cm.
20 cm
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That means that you can take 3 diameters of 20 cm
plus a little extra and wrap it around the
circle.
20 cm
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So the circumference is 3.14 x 20 62.8 cm
20 cm
20 cm
20 cm
20 cm
2.8 cm
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SUMMARY
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A circle is a collection of points that are all
the same distance away from a starting point.
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The radius is the distance from the center of the
circle to any point ON the circle.
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The diameter is twice the length of the radius,
and the diameter cuts the circle into 2 equal
halves.
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The circumference is the perimeter or the length
around the outside of the circle.
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Pi is 3.14. This is the number of diameters that
it takes to make up the circumference.
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So you can calculate the circumference by
multiplying the length of the diameter by 3.14.
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Practice Time!
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1) Find the circumference of the circle.
12 cm
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1) Find the circumference of the circle.
12 x 3.14 37.68 cm
12 cm
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2) Find the circumference of the circle.
25 cm
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2) Find the circumference of the circle.
25 x 3.14 78.5 cm
25 cm
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3) Find the circumference of the circle.
15.4 cm
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3) Find the circumference of the circle.
15.4 x 3.14 48.356 cm
15.4 cm
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4) Find the circumference of the circle.
.45 cm
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4) Find the circumference of the circle.
.45 x 3.14 1.413 cm
.45 cm
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5) Find the circumference of the circle.
7 cm
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5) Find the circumference of the circle.
2 x 7 x 3.14 43.96 cm
7 cm
You need to first double the radius to get the
diameter.
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6) Find the circumference of the circle.
12 cm
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6) Find the circumference of the circle.
2 x 12 x 3.14 75.36 cm
12 cm
You need to first double the radius to get the
diameter.
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7) Find the circumference of the circle.
31 cm
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7) Find the circumference of the circle.
2 x 31 x 3.14 194.68 cm
31 cm
You need to first double the radius to get the
diameter.
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8) Find the circumference of the circle.
.8 cm
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8) Find the circumference of the circle.
2 x .8 x 3.14 5.024 cm
.8 cm
You need to first double the radius to get the
diameter.
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The End!