Geometry 7­4 Surface Area Cylinders.notebook

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Title Page

Surface Area ­ Cylinder • Students will use the net of a cylinder to determine formulas for total

and lateral surface of a cylinder.• Students will write, solve and model equations involving surface

area of a cylinder.

8.7B ­ Use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders

TEKs

Warm­Up

Geometry

75o70o 35o

90o

Identify the pair of angles.3. x

y

4. xy

Find the surface area of the prism.1. 2.

3.

4.The surface area of a rectangular prism is 25 ft2. If each side is tripled, what is the new area?

4 m

6 m

7 m

4 in

25 22550 75

answer

1. 96 units2 2. 188 units2 3. 158 in 2

4. C

Homework Answers

1. A = 8 • 5 = 40 in.2; 2 • 8 • 5 = 80 in.2

2. A = 5 • 3 = 15 in.2; 2 • 5 • 3 = 30 in.2

3. A = 8 • 3 = 24 in.2; 2 • 8 • 3 = 48 in.2

4. S = 80 + 30 + 48 = 158 in.2; 158 in.25. 158 in2

6. 340 in2

7. 48 cm2

8. 88 in.2

9. 152 in2 10. 4 cubes11. The surface area will be 4 times as great. Sample answer: Since you are finding area and you multiply each dimension by 2, the area will be multiplied by 2 × 2, or 4.

Maintain Your Skills

1. A2. D

Practice Answers

Math Humor

What is the best dessert in the Math Teacher's Cafe?

A slice of cherry pi.

Math Humor

Introduction

How many bases? How many lateral surfaces?

What is the word that describes how much the can holds? What is the word that describes the paper label?

Geometry 7­4 Surface Area Cylinders.notebook

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Introduction

How many squares are in the rectangle and 2 circles?

Move to check your answer.

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3 4

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Labsheet

3.0

Cut and tape Labsheet in your journal

S = 2 rh + 2 r2Radius height

π πRadius

2. Determine the surface area using the formula.

Milton’s Chocolate Factory is creating a new package for their chocolate candies. They are considering a cylinder as shown.

1. Determine the surface area using the net.

Area Top Circle (πr2): ________________Area Bottom Circle (πr2): ________________ Circumference (2rπ): ________Area Lateral (C)(h): __________________TOTAL (Add Areas):

Radius: _____________________Height of prism: ______________TOTAL:

Pull

Pull

Area Top Circle (πr2): 3.14 x 1.52 = 7.065Area Bottom Circle (πr2): 3.14 x 1.52 = 7.065Circumference (2rπ): 2 x 1.5 x 3.14 = 9.42Area Lateral (C)(h): 9.42 x 10 = 94.2TOTAL: 108.33 cm2

Friend Transition

Find a friend and them how to find the difference between a

prism and a cylinder.

Would You Rather?

or only be able to shout?

Only be able to whisper...

Notes

_____ Surface Area Cylinders Date

1. What is the surface area of a cylinder?

• sum of area of 2 circularbases & lateral surface

• answer in units squared

lateral surface

Notes

2. How to find the surface area of a cylinder?

3 m

5 m

2(π x 3 x 3) + (6 x π x 5)= 18π + 30π = 48π= 56.52 + 94.2= 150.72 m2

S = 2 rh + 2 r2Radius height

π πRadius

• from a net ­ find area of all sides and add

• from the formula

Geometry 7­4 Surface Area Cylinders.notebook

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Notes

3. What is changing dimensions?

• how total area changes

• radius has bigger impact than height

9 in

4 in

3 in

2 in

S = 2 rh + 2 r2doubles doubles

π πquadruples

Application

Pull

Pull

Activity

r = 1 cm

circumference

area

d = 1yd

circumference

area

r = 3 m

circumference

area

d = 3 in

area

circumference

d = 2 ft

circumference

area

Homework

Practice

Surface Area of Cylinders Worksheet

How many faces?How many faces?

Closing Questions

Closing Questions

What is the lateral surface?

What is the formula for area of a circle?

(A = πr2)

(Circumference x height)