Geometry 7­4 Surface Area Cylinders.notebook
Surface Area ­ Cylinder Geometry
• 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.
TEKs
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 Find the surface area of the prism.
2.
1.
7 m
3.
4 m
4 in
6 m
Identify the pair of angles.
3.
x
4.
x
y
answer
y
4.
The surface area of a rectangular prism is 25 ft2. If each side is tripled, what is the new area?
225
70o
35o 25
75
90o 50
75o
Title Page
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.
5.
S = 80 + 30 + 48 = 158 in.2; 158 in.2
158 in2
6.
340 in2
7.
48 cm2
8.
88 in.2
1. 96 units2 2. 188 units2 3. 158 in 2
4. C Warm­Up
Practice Answers
Maintain Your Skills
1.
2.
A
D
9. 152 in2 10. 4 cubes
11. 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.
Homework Answers
Math Humor
What is the best dessert in
the Math Teacher's Cafe?
A slice of cherry pi.
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?
Math Humor
Introduction
1
Geometry 7­4 Surface Area Cylinders.notebook
How many squares are in the rectangle and 2 circles?
Cut and tape Labsheet in your journal
Milton’s Chocolate Factory is creating a new package for their chocolate candies. They are considering a cylinder as shown.
3.0
Move to check your answer.
1. Determine the surface area using the net.
Area Top Circle (πr2)
Area Bottom Circle (
Area Top Circle (πr2): ________________
Pull
Area Bottom Circle (πr2): ________________
Circumference (2rπ): ________
Circumference (2rπ):
Area Lateral (C)(h): 9
TOTAL: 108.33 c
Area Lateral (C)(h): __________________
TOTAL (Add Areas): 1
1
2
3
4
8
15
2
9
16
3
10
17
4
11
18
5
12
19
6
13
20
7
14
21
≈29
2. Determine the surface area using the formula.
Radius: _____________________
Height of prism: ______________
TOTAL:
1
2
3
4
π
S = 2 rh + 2 r
π 2
Radius
height
Introduction
Radius
Labsheet
Only be able to whisper...
or only be able to shout? Find a friend and them how to find the difference between a prism and a cylinder.
Friend Transition
Would You Rather?
_____ Surface Area Cylinders Date
1. What is the • sum of area of 2 circular
bases & lateral surface
surface area of a cylinder? • answer in units squared
lateral surface
Notes
2. How to find the surface area of a cylinder?
π
S = 2 rh + 2 r
π 2
Radius
height
• from a net ­ find area of all sides and add
• from the formula
3 m
Radius
5 m
2(π x 3 x 3) + (6 x π x 5)
= 18π + 30π = 48π
= 56.52 + 94.2
= 150.72 m2
Notes
2
Geometry 7­4 Surface Area Cylinders.notebook
•
3. What is changing dimensions? •
how total area changes
radius has bigger impact than height
π
S = 2 rh + 2 r
π 2
doubles
quadruples
doubles
4 in
2 in
3 in
9 in
Pull
Notes
Application
How many faces?
d = 3 in
d = 2 ft
r = 1 cm
Practice
area
area
area
circumference
circumference
circumference
r = 3 m
Surface Area of
Cylinders Worksheet
d = 1yd
area
area
circumference
circumference
Activity
Homework
Closing Questions
What is the formula for area of a circle?
(A = πr2) What is the lateral surface ? (Circumference x height)
Closing Questions
3