Learn to find the area of circles'

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Learn to find the area of circles.
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A circle can be cut into equal-sized sectors and
arranged to resemble a parallelogram. The height
h of the parallelogram is equal to the radius r
of the circle, and the base b of the
parallelogram is equal to one-half the
circumference C of the
circle.
So the area of
the parallelogram can be written as
1 2
A bh, or A
Cr.
1 2
Since C 2?r, A
(2?r)r ?r2.
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AREA OF A CIRCLE
The area A of a circle is the product of ? and
the square of the circles radius r.
r
A ?r2

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Additional Example 1A Finding the Area of a
Circle
Find the area of the circle to the nearest tenth.
Use 3.14 for ?.
A ?r2
A.
Use the formula.
7 cm
A ? 3.14 72
Substitute 7 for r.
A ? 3.14 49
Evaluate the power.
Multiply.
A ? 153.86
The area of the circle is about 153.9 cm2.
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Additional Example 1B Finding the Area of a
Circle
Find the area of the circle to the nearest tenth.
Use 3.14 for ?.
A ?r2
B.
Use the formula.

A ? 3.14 92
18 ft
Substitute 9 for r.
A ? 3.14 81
Evaluate the power.
Multiply.
A ? 254.34
The area of the circle is about 254.3 ft2.
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Try This Example 1A
Find the area of the circle to the nearest tenth.
Use 3.14 for ?.
A ?r2
A.
Use the formula.
A ? 3.14 102
10 cm
Substitute 10 for r.
A ? 3.14 100
Evaluate the power.
Multiply.
A ? 314
The area of the circle is about 314 cm2.
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Try This Example 1B
Find the area of the circle to the nearest tenth.
Use 3.14 for ?.
A ?r2
B.
Use the formula.

12 ft
A ? 3.14 62
Substitute 6 for r.
A ? 3.14 36
Evaluate the power.
Multiply.
A ? 113.04
The area of the circle is about 113.0 ft2.
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Additional Example 2 Application
Park employees are fitting a top over a circular
drain in the park. If the radius of the drain is
14 inches, what is the area of the top that will
cover the drain? Use
22 7
for ?.
A ? r2
Use the formula for the area of a circle.
22 7
A ?
142
Substitute. Use 14 for r.
28
22 7
196
A ?

Evaluate the power.
1
A ? 22 28
Multiply.
A ? 616
The area of the top that will cover the drain is
about 616 in2.
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Try This Example 2
Albert was designing a cover for a spa. If the
radius of the spa is 7 ft, what is the area of
the cover that will be made? Use
22 7
for ?.
A ? r2
Use the formula for the area of a circle.
22 7
A ?
72
Substitute. Use 7 for r.
7
22 7
49
A ?

Evaluate the power.
1
A ? 22 7
Multiply.
A ? 154
The area of the top that will cover spa is about
154 ft2.
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Additional Example 3 Application
A golf course is irrigated with sprinklers that
spray in a circle. If a sprinkler waters a
circular area with a radius of 25 feet, how many
square feet does the sprinkler cover? Round your
answer to the nearest whole number.
A ? r2
Use the formula for the area of a circle.
A ? 252

Substitute. Use 25 for r.
Use a calculator.
A ? 1963.495408
25
?
?
x2
Round.
A ? 1,963
The sprinkler covers about 1,963 ft2.
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Try This Example 3
Janet had a circular fish pond in her back yard.
She wanted to find the surface area of the pond.
If it had a radius of 13 feet, what is its
surface area in square feet? Round your answer to
the nearest whole number.
A ? r2
Use the formula for the area of a circle.
A ? 132

Substitute. Use 13 for r.
Use a calculator.
A ? 530.9216
13
?
?
x2
Round.
A ? 531
The pond has a surface area of about 531 ft2.
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Insert Lesson Title Here
Lesson Quiz
Find the area of each circle, to the nearest
tenth. Use 3.14 for ?. 1. 3. The bulls-eye
on a target has a diameter of 2 in. What is the
area of the bulls-eye to the nearest tenth? Use
3.14 for ?. 4. A round table cloth has a radius
of 36 in. What is the area of the table cloth?
Use 3.14 for ?. Round your answer to the nearest
tenth.
2.
9 ft
8 ft


63.6 ft2
201.0 ft2
3.1 in2
4,069.4 in2