Holt CA Course 1

10-2Circles and Circumference

Warm UpWarm Up

Lesson PresentationLesson Presentation

California StandardsCalifornia Standards

PreviewPreview

Holt CA Course 1

10-2Circles and Circumference

Warm UpThe length and width of a rectangle are each multiplied by 5. Find how the perimeter of the rectangle changes.

The perimeter is multiplied by 5.

Holt CA Course 1

10-2Circles and Circumference

MG1.1 Understand the concept of a constant such as ; know the formulas for the circumference and area of a circle.Also covered: AF1.1, AF3.1, AF3.2, MG1.2

California Standards

Holt CA Course 1

10-2Circles and Circumference

Vocabulary

circlecenterradius (radii)diametercircumferencepi

Holt CA Course 1

10-2Circles and Circumference

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

Center

Holt CA Course 1

10-2Circles and Circumference

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

CenterRadius

Holt CA Course 1

10-2Circles and Circumference

Diameter A line segment that passes through the center of the circle and has both endpoints on the circle. Notice that the length of the diameter is twice the length of the radius, d = 2r.

CenterRadius

Diameter

Holt CA Course 1

10-2Circles and Circumference

Circumference The distance around a circle.

CenterRadius

Diameter

Circumference

Holt CA Course 1

10-2Circles and 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

The decimal representation of pi starts with 3.14159265 . . . and goes on forever without repeating. Most people approximate using

either 3.14 or .22 7

Holt CA Course 1

10-2Circles and Circumference

Use as an estimate for when the

diameter or radius is a multiple of 7.

22 7

Helpful Hint

Holt CA Course 1

10-2Circles and Circumference

Because , you can

multiply both sides of the equation by d to get a formula for circumference. You can also substitute 2r for d because d = 2r.

Cd

= Cd

=

Cd

· d = · d

C = d

C = (2r) = 2r

Holt CA Course 1

10-2Circles and Circumference

Additional Example 1: Naming Parts of a Circle

Name the circle, a diameter, and three radii.

N

The center is point Z, so this is circle Z.

LM is a diameter.

ZL, ZM, and ZN are radii.

M

ZL

Holt CA Course 1

10-2Circles and CircumferenceAdditional Example 2: Application

A skydiver is laying out a circular target for his next jump. Estimate the circumference of

the target by using as an estimate for .

C = d

C • 10.5

C 33 ft

The circumference of the target is about 33 feet.

Use the formula.

Replace with and d with 10.5.

10.5 ft

22 7

22 7

22 7

Holt CA Course 1

10-2Circles and CircumferenceAdditional Example 3: Using the Formula for the

Circumference of a Circle

A. Find the missing value to the nearest hundredth. Use 3.14 as an estimate for .

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

Holt CA Course 1

10-2Circles and CircumferenceAdditional Example 3: Using the Formula for the

Circumference of a Circle

B. Find each missing value to the nearest hundredth. Use 3.14 as an estimate for .

r = 5 cm; C = ?

C = 2r

C 2 • 3.14 • 5

C 31.40 cm

Write the formula.

Replace with 3.14 and r with 5.

5 cm

Holt CA Course 1

10-2Circles and Circumference

Check It Out! Example 1

Name the circle, a diameter, and three radii.

The center is point D, so this is circle D.

IG is a diameter.

DI, DG, and DH are radii.

G

H

DI

Holt CA Course 1

10-2Circles and CircumferenceCheck It Out! Example 2

A concrete chalk artist is drawing a circular design. Estimate the circumference of the

chalk design by using as an estimate for .

C = d

C • 14

C ≈ 44 in.The circumference of the chalk design is about 44 inches.

Use the formula.

Replace with and d with 14.

22 7

22 7

22 7

14 in.

1

2

Holt CA Course 1

10-2Circles and CircumferenceCheck It Out! Example 3

A. Find the missing value to the nearest hundredth. Use 3.14 as an estimate for .

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

Holt CA Course 1

10-2Circles and Circumference

Check It Out! Example 3

B. Find each missing value to the nearest hundredth. Use 3.14 as an estimate for .

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

Holt CA Course 1

10-2Circles and Circumference

Check It Out! Example 3

C. Find each missing value to the nearest hundredth. Use 3.14 as an estimate for .

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.

Holt CA Course 1

10-2Circles and CircumferenceLesson Quiz

Find the circumference of each circle. Use 3.14 as an estimate for .

1. 2.

3. Find the circumference of a circle with

diameter of 20 feet. Use 3.14 as an estimate

t for .

C ≈ 25.12 in. C ≈ 18.84 in.

C ≈ 62.8 ft