Finding the Area of a Circle: Lesson
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"The Area Formula"

To find the area of a circle use the following formula:
A = Π x r2
("r" is the radius of the circle)

In New York State, we leave the answer in "pi" form,

 meaning we don't multiply by 3.14.  You will see examples of "pi form" below.
 

Let's start with an easy example.



A circular garden has a radius of 15 feet.  What is the area of the garden?
 

Using the area formula simply plug in the value of "r", and remember rČ = r x r
A = Π x r2
A = Π(15)2

A = 225Π
A = 225Π square feet
 

See how easy??


How much greater is the area of a circle whose radius is 8 feet than a circle whose radius is 4 feet?
Do you think twice as large???
Hmmm....take a guess before you look at the solution below.
 

Let's look at the first circle:
radius = 8 feet
A = Π r2
A =Π(8)2
      A = Π  x 8 x 8
A =
Π(64)
           A = 64
Π square feet

Now, the second circle:
radius = 4 feet
A = Π r2

A =
Π (4)2
A = 16
Π
             A = 16
Π square feet

Now, divide 64 by 16
The result is "4"
That's right, a circle of radius 8 is
4 times greater than a circle of radius 4.

 

Now let's look at a tough one..



A circular walkway surrounds a circular piece of ground.
The walkway is exactly 4 feet wide.  If the radius of the circular piece of ground is 33 feet, find the area of the walkway.

       Before diving into this one let's think about what is really going on. What we really have here is a larger circle, of which we can only see the walkway, with a smaller circle, the piece of ground, being placed directly on top of the larger one.  So to find the area of the walkway, all we have to do is calculate the area of the larger circle, and then subtract the area of the smaller circle from it.  That will leave us with just the area of the walkway!
Let's get started:
Area of larger circle:
Remember, the walkway is 3 feet wide all the way around.  That makes the radius of the larger circle 3 feet longer than that of the smaller circle.
r = 36 feet
A = Π r2

A = Π(36)2
A = 1296Π
            A = 1296Π square feet
Repeat the process for the smaller circle:
r = 33 feet
A = Π(33)2
A = 1089Π
          A =1089Π square feet
To find the area of just the walkway we need to
subtract these two areas:
1296Π - 1089Π =
Area of walkway = 207
Π  square feet.
 

 Practice on your own....
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