8-7 Circles and Circumference Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

8-7 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


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 1Point D is the center of the circle. Name the circle, two chords, a diameter, and three radii.

The circle is circle D.

Radii = DI, DG, and DH are

diameter = GI

chords = GI and GH

GD

H

I


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

The circumference of the target is about 24 feet.


C = d

C 3 • 4

C 12 ft

A carpenter is building a circular tabletop. Estimate the circumference of the tabletop by rounding to 3.

Check It Out: 2A

What is the circumference of the tabletop if the diameter is 4 feet?


C = 2r

C 2 • 3 • 3

C 18 ft

carpenter is building a circular tabletop. Estimate the circumference of the tabletop by rounding to 3.

What is the circumference of the tabletop if the radius is 3 feet?

Check It Out: 2B


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 22/7 for pi.

r = 7 cm; C = ?

C = 2r

C 2 • 22/7 • 7

C 44 cm

Write the formula.

Replace with 22/7 and r with 7.

7 cm


Check It Out: Example 3A

Find the missing value to the nearest hundredth. Use 3.14 or 22for pi.

C = ?7

D = 2.8

C = πdC ≈ 3.14 • 2.8C ≈ 8.79 m


Check It Out: Example 3B

Find the missing value to the nearest hundredth. Use 3.14 or 22for pi.

r = ?7

C = 88 cm

C = 2πr

88 ≈ 2 r

88 ≈ 44 r

r ≈ 14 cm

227__

7


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


Documents

8-7 Circles and Circumference Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes