9-8 circles and circumference warm up warm up lesson presentation lesson presentation problem of the...

9-8 Circles and Circumference

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


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.


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


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


Vocabulary

circlecenterchorddiameterradius (radii)circumferencepi


A circle is the set of all points in a plane that are the same distance from a given point, called the center.

Center


Radius (plural: radii). A line segment with one endpoint at the center of the circle and the other endpoint on the circle.

CenterRadius


A diameter is a chord that passes through the center of the circle. Diameters are the longest chords in a circle.

CenterRadius

Diameter


A chord is a line segment that has both endpoints on the circle.

CenterRadius

Diameter

Chord


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.

LN and LM are chords.

M

ZL

ZL, ZM, and ZN are radii.


Check It Out: Example 1

Name the circle, a diameter, and three radii.

The circle is circle D.

DI, DG, and DH are radii.

G

H

DI

IG is a diameter.

IG and IH are chords.


The distance around a circle is called the circumference.

CenterRadius

Diameter

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

=


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. Most people estimate using either 3.14 or .22

7


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


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


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


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


Additional Example 3C: Using the Formula for the Circumference of a Circle


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.


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


Check It Out: Example 3B


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


Check It Out: Example 3C


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.


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson Quiz

Find the circumference of each circle. Use 3.14 for .

1. 2.

3. Find the circumference of a circle with a

diameter of 20 feet. Use 3.14 for .

C = 25.12 in. C = 18.84 in.

8 in.

62.8 ft

3 in.


1. Identify the circumference of the given circle. Use 3.14 for .

A. 31.14 in. B. 31.21 in.

C. 31.33 in. D. 31.4 in.


10 in.


2. Identify the circumference of the given circle. Use 3.14 for .

A. 37.54 in. B. 37.68 in.

C. 37.81 in. D. 37.93 in.


6 in.


3. Identify the circumference of a circle with a diameter of 26 feet. Use 3.14 for .

A. 81.64 ft B. 81.73 ft

C. 81.86 ft D. 81.92 ft


9-8 circles and circumference warm up warm up lesson presentation lesson presentation problem of the...

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