View
221
Download
1
Category
Tags:
Preview:
Citation preview
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.
Course 1
10-5 Circles
Vocabulary
circlecenterradius (radii)diametercircumferencepi
Insert Lesson Title Here
Course 1
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
Course 1
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
Course 1
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
Course 1
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
Course 1
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
Course 1
10-5 Circles
The distance around a circle is called the circumference.
CenterRadius
Diameter
Circumference
Course 1
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
=
Course 1
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
Course 1
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
Course 1
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
Course 1
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
Course 1
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
Course 1
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.
Course 1
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.
Course 1
10-5 Circles
The formula for the area of a circle is
A = r2 OR
A = 3.14(r)(r)
Course 1
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
Course 1
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
Course 1
10-5 Circles
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.
Course 1
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
Recommended