How to calculate the area of a circle.

1
How to calculate the area of a circle.
Its as easy as pi.
2
Lets first make sure that we understand the
difference between circumference and area.
3
The circumference of a circle is the perimeter of
the circle.
4
Imagine that the circle is straightening itself
out.
5
(No Transcript)
6
(No Transcript)
7
(No Transcript)
8
The length of this line segment is the
circumference of the circle.
314 cm
9
The circumference is the same length as 3
diameters plus .14 of another diameter.
10
So, circumference diameter x 3.14
11
(No Transcript)
12
(No Transcript)
13
(No Transcript)
14
(No Transcript)
15
Does this look familiar?
16
O.K., now its time to move forward with some new
stuff.
17
How in the world would you find the area of a
circle?
18
Remember, area is always measured in square units.
19
Remember that the area of a rectangle is length x
width because youre calculating the total number
of squares inside of the rectangle.
2
4
20
Thats fine and dandy, but a circle is not a
polygon. It does not have straight sides it has
curves.
21
How are we going to get around these curves?
22
Imagine chopping up the circle as if it were a
pizza.
23
Now, lets rearrange our pizza into another
shape.
24
(No Transcript)
25
(No Transcript)
26
(No Transcript)
27
(No Transcript)
28
(No Transcript)
29
(No Transcript)
30
(No Transcript)
31
PRESTO!
32
Great Mr. Dunlap! But what in the world is this?
33
Believe it or not, this is really our friend
the parallelogram. And, we know how to calculate
the area of a parallelogram.
34
Rats! He always has an answer for everything.
35
Area Base x Height
Height
Base
36
To find the area of the circle (which is now a
parallelogram), we just need to multiply the Base
by the Height.
Height
Base
37
Wait a minute! The height of this parallelogram
is really the radius of the circle.
Radius
Base
38
Wait a minute! The Base is really 1/2 of the
circumference.
Radius
1/2 of Circumference
39
Wait a minute! The circumference is really
Diameter x ?
Radius
1/2 of Diameter x ?
40
Wait a minute! 1/2 of a Diameter is really a
Radius.
Radius
Radius x ?
41
So if we multiply the Base x Height
Height
Base
42
We are really multiplyingRadius x Radius x ?
Radius
Radius x ?
43
Practice Time!
44
1) Now lets try this formula. Find the area of
this circle.
5 cm
45
5 x 5 x 3.14 78.5 square cm
5 cm
46
2) Find the area of this circle.
6 cm
47
6 x 6 x 3.14 113.04 square cm
6 cm
48
3) Find the area of this circle.
9 cm
49
9 x 9 x 3.14 254.34 square cm
9 cm
50
4) Find the area of this circle.
20 cm
51
10 x 10 x 3.14 314 cm2
Make sure that you use the radius of the circle.
20 cm
52
5) Find the area of this circle.
14 cm
53
7 x 7 x 3.14 153.86 cm2
Make sure that you use the radius of the circle.
14 cm
54
6) Find the area of this circle.
22 cm
55
11 x 11 x 3.14 379.94 cm2
22 cm
56
Area Radius x Radius x ?
Its as easy as pi.