Area of Circles

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By: deasabathulachak (63 month(s) ago)

very good

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How to calculate the area of a circle.:

How to calculate the area of a circle. It’s as easy as pi.

Let’s first make sure that we understand the difference between circumference and area.:

Let’s first make sure that we understand the difference between circumference and area.

The circumference of a circle is the perimeter of the circle. :

The circumference of a circle is the perimeter of the circle.

Imagine that the circle is straightening itself out.:

Imagine that the circle is straightening itself out.

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The length of this line segment is the circumference of the circle. 314 cm

The circumference is the same length as 3 diameters plus .14 of another diameter.:

The circumference is the same length as 3 diameters plus .14 of another diameter.

So, circumference = diameter x 3.14:

So, circumference = diameter x 3.14

Does this look familiar?:

Does this look familiar?

O.K., now it’s time to move forward with some new stuff.:

O.K., now it’s time to move forward with some new stuff.

How in the world would you find the area of a circle?:

How in the world would you find the area of a circle?

Remember, area is always measured in square units.:

Remember, area is always measured in square units.

Remember that the area of a rectangle is length x width because you’re calculating the total number of squares inside of the rectangle. :

Remember that the area of a rectangle is length x width because you’re calculating the total number of squares inside of the rectangle. 2 4

That’s fine and dandy, but a circle is not a polygon. It does not have straight sides; it has curves.:

That’s fine and dandy, but a circle is not a polygon. It does not have straight sides; it has curves.

How are we going to get around these curves?:

How are we going to get around these curves?

Imagine chopping up the circle as if it were a pizza.:

Imagine chopping up the circle as if it were a pizza.

Now, let’s rearrange our “pizza” into another shape. :

Now, let’s rearrange our “pizza” into another shape.

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PRESTO!

Great Mr. Dunlap! But what in the world is this?:

Great Mr. Dunlap! But what in the world is this?

Believe it or not, this is really our “friend” the parallelogram. And, we know how to calculate the area of a parallelogram.:

Believe it or not, this is really our “friend” the parallelogram. And, we know how to calculate the area of a parallelogram.

Rats! He always has an answer for everything.:

Rats! He always has an answer for everything.

Area = Base x Height:

Area = Base x Height Base Height

To find the area of the circle (which is now a parallelogram), we just need to multiply the Base by the Height.:

To find the area of the circle (which is now a parallelogram), we just need to multiply the Base by the Height. Base Height

Wait a minute! The height of this “parallelogram” is really the radius of the circle.:

Base Radius Wait a minute! The height of this “parallelogram” is really the radius of the circle.

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1/2 of Circumference Radius Wait a minute! The Base is really 1/2 of the circumference.

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1/2 of Diameter x  Radius Wait a minute! The circumference is really Diameter x 

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Radius x  Radius Wait a minute! 1/2 of a Diameter is really a Radius.

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Base Height So if we multiply the Base x Height

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We are really multiplying Radius x Radius x  Radius x  Radius

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Practice Time!

1) Now let’s try this formula. Find the area of this circle.:

1) Now let’s try this formula. Find the area of this circle. 5 cm

5 x 5 x 3.14 = 78.5 square cm:

5 x 5 x 3.14 = 78.5 square cm 5 cm

2) Find the area of this circle.:

2) Find the area of this circle. 6 cm

6 x 6 x 3.14 = 113.04 square cm:

6 x 6 x 3.14 = 113.04 square cm 6 cm

3) Find the area of this circle.:

3) Find the area of this circle. 9 cm

9 x 9 x 3.14 = 254.34 square cm:

9 x 9 x 3.14 = 254.34 square cm 9 cm

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4) Find the area of this circle. 20 cm

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10 x 10 x 3.14 = 314 cm 2 20 cm Make sure that you use the radius of the circle.

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5) Find the area of this circle. 14 cm

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7 x 7 x 3.14 = 153.86 cm 2 14 cm Make sure that you use the radius of the circle.

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6) Find the area of this circle. 22 cm

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11 x 11 x 3.14 = 379.94 cm 2 22 cm

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Area = Radius x Radius x  It’s as easy as pi.

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