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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.
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Let's start with
an easy example.
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A circular garden has
a radius of 15 feet. What is the area of the garden?
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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
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See how easy??
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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.
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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 = 64Π 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.
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Now let's look
at a tough one..
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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.
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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 = 207Π square feet.
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