10-5 Circles

Course 1

HOMEWORK & Learning GoalHOMEWORK & Learning Goal

AIMS PrepAIMS Prep

Lesson PresentationLesson Presentation

Chapter 10 Section 46th M. HOMEWORK Answers

Page 512-513

#1-4 and

#11-14 (SR)

Chapter 10 Section 56th Grade Math HOMEWORK

Page 518#6-9 (Circumference)

& #10-12 (Area)

Our Learning Goal

Students will be able to find the perimeter and area of polygons; find the area and circumference of circles and find the surface

area and volume of 3D shapes.

Our Learning Goal Assignments• Learn to find the perimeter and missing side lengths of a

polygon.

• Learn to estimate the area of irregular figures and to find the area of rectangles, triangles, and parallelograms.

• Learn to break a polygon into simpler parts to find its area.

• Learn to make a model to explore how area and perimeter are affected by changes in the dimensions of a figure.

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

• Learn to name solid figures.

• Learn to find the surface areas of prisms, pyramids, and cylinders.

• Learn to estimate and find the volumes of rectangular prisms and triangular prisms.

• Learn to find volumes of cylinders.

Today’s Learning Goal Assignment

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

HTTP://WWW.BRAINPOP.COM/MATH/NUMBERSANDOPERATIONS/PI/

BRAINPOP - Pi

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

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

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

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

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 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 OR

A = 3.14(r)(r)

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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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Don’t forget your proper heading! Trade & Grade!

10-5 Lesson QuizFind 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

6th Grade AIMS Prep

Recall some test-taking tricks that you use to “win” on the AIMS Math.

Use at least one to solve the following example!

AIMS Example 2