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 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

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

Vocabulary

circlecenterradius (radii)diametercircumferencepi

Insert Lesson Title Here

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

Center

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

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

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

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

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. We estimate pi using either 3.14

or .22 7

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

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

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.

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

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

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.

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

A = r2

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

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

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.