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.

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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

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10-5 Circles

Learn to identify the parts of a circle and to find the circumference and area of a circle.

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10-5 Circles

Vocabulary

circlecenterradius (radii)diametercircumferencepi

Insert Lesson Title Here

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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

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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

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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

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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.

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10-5 Circles

The formula for the area of a circle is A = r2.

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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

Lesson Quiz

Find the circumference and area of each circle. Use 3.14 for .

1. 2.

3. Find the area of a circle with a diameter of 20

feet. Use 3.14 for .

C = 25.12 in.

Insert Lesson Title Here

C = 18.84 in.

8 in.

314 ft2

A = 50.24 in2 A = 28.26 in2

3 in.

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10-5 Circles