How to calculate the area of a circle. Its as easy as pi.
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Transcript of How to calculate the area of a circle. Its as easy as pi.
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 .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. 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.
And, we know how to calculate the area of a
parallelogram.
Rats! He always has an answer for everything.
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.
Base
Height
Base
Radius
Wait a minute! The height of this “parallelogram” is really the radius
of the circle.
1/2 of Circumference
Radius
Wait a minute! The Base is really 1/2 of the circumference.
1/2 of Diameter x
Radius
Wait a minute! The circumference is
really Diameter x
Radius x
Radius
Wait a minute! 1/2 of a Diameter is really a Radius.
Base
Height
So if we multiply the Base x Height
We are really multiplying
Radius x Radius x
Radius x
Radius
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
10 x 10 x 3.14 = 314 cm2
20 cm
Make sure that you use the radius of
the circle.
5) Find the area of this circle.
14 cm
7 x 7 x 3.14 = 153.86 cm2
14 cm
Make sure that you use the radius of
the circle.
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.