How to calculate the area of a circle.

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Presentation transcript:

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.

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

Imagine that the circle is straightening itself out.

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

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

So, circumference = diameter x 3.14

Does this look familiar?

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?

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. 2 4

That’s fine and dandy, but a circle is not a polygon 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?

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

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

PRESTO!

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

Believe it or not, this is really our “friend” the 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.

Area = Base x Height Height Base

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

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

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

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

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

So if we multiply the Base x Height

We are really multiplying Radius x Radius x 

Practice Time!

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 cm

2) Find the area of this circle. 6 cm

6 x 6 x 3.14 = 113.04 square cm 6 cm

3) Find the area of this circle. 9 cm

9 x 9 x 3.14 = 254.34 square cm 9 cm

4) Find the area of this circle. 20 cm

Make sure that you use the radius of the circle. 10 x 10 x 3.14 = 314 cm2 Make sure that you use the radius of the circle. 20 cm

5) Find the area of this circle. 14 cm

Make sure that you use the radius of the circle. 7 x 7 x 3.14 = 153.86 cm2 Make sure that you use the radius of the circle. 14 cm

6) Find the area of this circle. 22 cm

11 x 11 x 3.14 = 379.94 cm2 22 cm

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