10-1 circles and circumference. a circle is the set of all points in a plane that are the same...
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10-1 Circles and Circumference
A circle is the set of all points in a plane that are the same distance from a given point, called the center.
Center
10-1Circles and Circumference
A line segment with one endpoint at the center of the circle and the other endpoint on the circle is a radius (plural: radii).
CenterRadius
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10-1Circles and Circumference
A diameter is a line segment that passes through the center of the circle and has both endpoints on the circle. The length of the diameter is twice the length of the radius.
CenterRadius
Diameter
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10-1Circles and Circumference
Additional Example 1: Naming Parts of a Circle
Name the circle, a diameter, and three radii.
NThe circle is circle Z.
LM is a diameter.
ZL, ZM, and ZN are radii.
M
ZL
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10-1Circles and Circumference
Check It Out: Example 1
Name the circle, a diameter, and three radii.
The circle is circle D.
IG is a diameter.
DI, DG, and DH are radii.
G
H
DI
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10-1Circles and Circumference
The distance around a circle is called the circumference.
CenterRadius
Diameter
Circumference
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10-1Circles and Circumference
The ratio of the circumference to the diameter, , is the same for any circle. This
ratio is represented by the Greek letter , which is read “pi.”
Cd
Cd
=
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10-1Circles and Circumference
The formula for the circumference of a circle is C = d, or C = 2r.
The decimal representation of pi starts with 3.14159265 . . . and goes on forever without repeating. We estimate pi using either 3.14
or .22 7
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10-1Circles and Circumference
Additional Example 2: Application
A skydiver is laying out a circular target for his next jump. Estimate the circumference of the target by rounding to 3.
C = d
C 3 • 8
C 24 ft
Write the formula.
Replace with 3 and d with 8.
8 ft
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10-1Circles and Circumference
Check It Out: Example 2
A second skydiver is laying out a circular target for his next jump. Estimate the circumference of the target by rounding to 3.
C = d
C 3 • 14
C 42 yd
Write the formula.
Replace with 3 and d with 14.
14 yd
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10-1Circles and Circumference
Additional Example 3A: Using the Formula for the Circumference of a Circle
Find the missing value to the nearest hundredth. Use 3.14 for pi.
d = 11 ft; C = ?
C = d
C 3.14 • 11
C 34.54 ft
Write the formula.
Replace with 3.14 and d with 11.
11 ft
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10-1Circles and Circumference
Additional Example 3B: Using the Formula for the Circumference of a Circle
Find each missing value to the nearest hundredth. Use 3.14 for pi.
r = 5 cm; C = ?
C = 2r
C 2 • 3.14 • 5
C 31.4 cm
Write the formula.
Replace with 3.14 and r with 5.
5 cm
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10-1Circles and Circumference
Additional Example 3C: Using the Formula for the Circumference of a Circle
Find each missing value to the nearest hundredth. Use 3.14 for pi.
C = 21.98 cm; d = ?
C = d
21.98 3.14d
7.00 cm d
Write the formula.
Replace C with 21.98 and with 3.14.
21.98 3.14d_______ _______
3.14 3.14 Divide both sides by 3.14.
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10-1Circles and Circumference
Check It Out: Example 3A
Find the missing value to the nearest hundredth. Use 3.14 for pi.
d = 9 ft; C = ?
C = d
C 3.14 • 9
C 28.26 ft
Write the formula.
Replace with 3.14 and d with 9.
9 ft
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10-1Circles and Circumference
Check It Out: Example 3B
Find each missing value to the nearest hundredth. Use 3.14 for pi.
r = 6 cm; C = ?
C = 2r
C 2 • 3.14 • 6
C 37.68 cm
Write the formula.
Replace with 3.14 and r with 6.
6 cm
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10-1Circles and Circumference
Check It Out: Example 3C
Find each missing value to the nearest hundredth. Use 3.14 for pi.
C = 18.84 cm; d = ?
C = d
18.84 3.14d
6.00 cm d
Write the formula.
Replace C with 18.84 and with 3.14.
18.84 3.14d_______ _______
3.14 3.14 Divide both sides by 3.14.
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10-1Circles and Circumference
Lesson Quiz
Find the circumference of each circle. Use 3.14 for .
1. 2.
3. Find the circumference of a circle with
diameter of 20 feet. Use 3.14 for .
C = 25.12 in.
Insert Lesson Title Here
C = 18.84 in.
8 in.
62.8 ft
3 in.
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10-1Circles and Circumference