10-5 Circles
Course 1
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
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.
Course 1
10-5 Circles
Problem of the Day
When using a calculator to find the height 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 height?1.3
Course 1
10-5 Circles
Learn to identify the parts of a circle and to find the circumference and area of a circle.
Course 1
10-5 Circles
Vocabulary
circlecenterradius (radii)diametercircumferencepi
Insert Lesson Title Here
Course 1
10-5 Circles
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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10-5 Circles
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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10-5 Circles
A chord is a line segment with both endpoints on a circle. A diameter is a chord that passes through the center of the circle. The length of the diameter is twice the length of the radius.
CenterRadius
Diameter
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10-5 Circles
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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10-5 Circles
Try This: 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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10-5 Circles
The distance around a circle is called the circumference.
CenterRadius
Diameter
Circumference
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10-5 Circles
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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10-5 Circles
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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10-5 Circles
Additional Example 2A: Using the Formula for the Circumference of a Circle
Find the missing value to the nearest hundredth. Use 3.14 for pi.
A. 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
Course 1
10-5 Circles
Additional Example 2B: Using the Formula for the Circumference of a Circle
Find each missing value to the nearest hundredth. Use 3.14 for pi.
B. 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
Course 1
10-5 Circles
Additional Example 2C: Using the Formula for the Circumference of a Circle
Find each missing value to the nearest hundredth. Use 3.14 for pi.
C. 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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10-5 Circles
Try This: Example 2A
Find the missing value to the nearest hundredth. Use 3.14 for pi.
A. 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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10-5 Circles
Try This: Example 2B
Find each missing value to the nearest hundredth. Use 3.14 for pi.
B. 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
Course 1
10-5 Circles
Try This: Example 2C
Find each missing value to the nearest hundredth. Use 3.14 for pi.
C. 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.
Course 1
10-5 Circles
Additional Example 3: Using the Formula for the Area of a Circle
Find the area of the circle. Use for pi.
d = 42 cm; A = ?
Write the formula to find the area.A = r2
r = d ÷ 2r = 42 ÷ 2 = 21
The length of the diameter is twice the length of the radius.
Replace with and r with 21.22
7 __
A • 44122
7 __ Use the GCF to simplify.
63
A 1,386 cm2 Multiply.
22 7
A • 21222
7
1
42 cm
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10-5 Circles
Write the formula to find the area.A = r2
r = d ÷ 2r = 28 ÷ 2 = 14
The length of the diameter is twice the length of the radius.
Replace with and r with 14.22
7 __
A • 19622
7 __ Use the GCF to simplify.
28
A 616 cm2 Multiply.
Try This: Example 3
Find the area of the circle. Use for pi.
d = 28 cm; A = ?
22 7
A • 14222
7
1
28 cm
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10-5 Circles