8.7 Circumference and Area of Circles
Goal
Find the circumference and area of circles.
VOCABULARY
Circle, center A circle is the set of all points in a plane that
are the same distance from a given point, called the center
of the circle.
Radius The radius of a circle is the distance from the center
to a point on the circle. A segment whose endpoints are the
center of the circle and a point on the circle is also called a
radius.
Diameter The diameter of a circle is the distance across the
circle, through the center. The diameter is twice the radius.
A chord that passes through the center of the circle is also
called a diameter.
Circumference The circumference of a circle is the distance
around the circle.
Central angle An angle whose vertex is the center of a circle
is a central angle of the circle.
Sector A sector is a region of a circle determined by two
radii and a part of the circle.
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Geometry, Concepts and Skills Notetaking Guide • Chapter 8
CIRCUMFERENCE OF A CIRCLE
Words The circumference of a circle is the product of
π and the diameter or twice the product of π
and the radius .
Symbols C πd
Example 1
r
or C 2πr
Find the Circumference of a Circle
Find the circumference of the circle.
Solution
C 2πr
4 in.
Formula for circumference
2π( 4 )
Subtitute 4 for r.
8π
Simplify.
≈ 8 ( 3.14 )
Use 3.14 as an approximation for π.
25.13
Multiply.
Answer The circumference is about 25 inches.
Checkpoint Find the circumference of the circle. Round your
answer to the nearest whole number.
1.
2.
3.
6 cm
16 in.
9 ft
38 cm
57 ft
50 in.
AREA OF A CIRCLE
Words The area of a circle is the product of π and
the radius squared .
r
Symbols A πr 2
Lesson 8.7 • Geometry, Concepts and Skills Notetaking Guide
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Example 2
Find the Area of a Circle
Find the area of the circle.
Solution
A πr 2
7 cm
Formula for area of a circle
π( 7 ) 2
Substitute 7 for r.
( 49 )π
Simplify.
≈ 153.94
Use a calculator.
Answer The area is about 154 square centimeters.
Example 3
Use the Area of a Circle
Find the radius of a circle with an area
of 380 square feet.
r
A 380 ft 2
Solution
A πr 2
Formula for area of a circle
380 πr 2
Substitute the 380 for A.
120.96 ≈ r 2
11 ≈ r
Divide each side by π . Use a calculator.
Take the positive square root .
Answer The radius is about 11 feet.
Checkpoint In Exercises 4–6, find the area of the circle. Round
your answer to the nearest whole number.
4.
8 in.
5.
6.
12 ft
3 cm
201 in.2
28 cm2
113 ft2
7. Find the radius of a circle with an area of 113 square meters.
about 6 meters
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Geometry, Concepts and Skills Notetaking Guide • Chapter 8
Find the Area of a Sector
Example 4
Find the area of the shaded sector.
9m
120°
Solution
1. Find the area of the circle.
A πr 2 π( 9 )2 ≈ 254 square meters
2. Find the area of the sector. Let x be the area of the sector.
Measure of central angle
Area of sector
Area of entire circle
Measure of entire circle
120
360
254
x
Substitute.
( 360 )(x) ( 254 )( 120 )
Cross product property
360 x 30,480
Simplify.
x ≈ 84.67
Divide each side
by 360 .
Answer The area of the sector is about 85 square meters.
Checkpoint In Exercises 8 and 9, A represents the area of the
entire circle and x represents the area of the shaded sector.
Complete the proportion used to find the value of x. Do not
solve the proportion.
9. A 28 ft 2
8. A 22 m 2
x
22
180
x
180°
28
360
270
170°
360
Find the area of the shaded sector. Round your answer to the
nearest whole number.
10.
11.
12.
5 cm
2 ft
60°
2 ft 2
90°
20 cm 2
6 in.
135°
42 in. 2
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