9-8 circles and circumference course 1 warm up warm up lesson presentation lesson presentation...
TRANSCRIPT
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9-8 Circles and Circumference
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Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
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Warm UpThe length and width of a rectangle are each multiplied by 5. Find how the perimeter and area of the rectangle change.
The perimeter is multiplied by 5, and the area is multiplied by 25.
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Problem of the Day
When using a calculator to find the width of a rectangle whose length one knew, a student accidentally multiplied by 20 when she should have divided by 20. The answer displayed was 520. What is the correct width?1.3
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Learn to identify the parts of a circle and to find the circumference of a circle.
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Vocabulary
circlecenterradius (radii)diametercircumferencepi
Insert Lesson Title Here
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A circle is the set of all points in a plane that are the same distance from a given point, called the center.
Center
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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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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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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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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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The distance around a circle is called the circumference.
CenterRadius
Diameter
Circumference
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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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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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Formula to find the circumference of a circle:
C = d (d is the diameter)
Or
C= 2 r (r is the radius)
USE 3.14 for .
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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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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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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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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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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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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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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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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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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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