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Mary Pyo

Mary Pyo

Surface Area of a Cylinder

Slide Duration:

Table of Contents

I. Algebra and Decimals
Expressions and Variables

5m 57s

Intro
0:00
Vocabulary
0:06
Variable
0:09
Expression
0:48
Numerical Expression
1:08
Algebraic Expression
1:35
Word Expression
2:04
Extra Example 1: Evaluate the Expression
2:27
Extra Example 2: Evaluate the Expression
3:16
Extra Example 3: Evaluate the Expression
4:04
Extra Example 4: Evaluate the Expression
4:59
Exponents

5m 34s

Intro
0:00
What Exponents Mean
0:07
Example: Ten Squared
0:08
Extra Example 1: Exponents
0:50
Extra Example 2: Write in Exponent Form
1:58
Extra Example 3: Using Exponent and Base
2:37
Extra Example 4: Write the Equal Factors
4:26
Order of Operations

8m 40s

Intro
0:00
Please Excuse My Dear Aunt Sally
0:07
Step 1: Parenthesis
1:16
Step 2: Exponent
1:25
Step 3: Multiply and Divide
1:30
Step 4: Add and Subtract
2:00
Example: Please Excuse My Dear Aunt Sally
2:26
Extra Example 1: Evaluating Expression
3:37
Extra Example 2: Evaluating Expression
4:59
Extra Example 3: Evaluating Expression
5:34
Extra Example 4: Evaluating Expression
6:25
Comparing and Ordering Decimals

13m 37s

Intro
0:00
Place Value
0:13
Examples: 1,234,567.89
0:19
Which is the Larger Value?
1:33
Which is Larger: 10.5 or 100.5
1:46
Which is Larger: 1.01 or 1.10
2:24
Which is Larger: 44.40 or 44.4
4:20
Which is Larger: 18.6 or 16.8
5:18
Extra Example 1: Order from Least to Greatest
5:55
Extra Example 2: Order from Least to Greatest
7:56
Extra Example 3: Order from Least to Greatest
9:16
Extra Example 4: Order from Least to Greatest
10:42
Rounding Decimals

12m 31s

Intro
0:00
Decimal Place Value
0:06
Example: 12,3454.6789
0:07
How to Round Decimals
1:17
Example: Rounding 1,234.567
1:18
Extra Example 1: Rounding Decimals
3:47
Extra Example 2: Rounding Decimals
6:10
Extra Example 3: Rounding Decimals
7:45
Extra Example 4: Rounding Decimals
9:56
Adding and Subtracting Decimals

11m 30s

Intro
0:00
When Adding and Subtracting
0:06
Align the Decimal Point First
0:12
Add or Subtract the Digits
0:47
Place the Decimal Point in the Same Place
0:55
Check by Estimating
1:09
Examples
1:28
Add: 3.45 + 7 + 0.835
1:30
Find the Difference: 351.4 - 65.25
3:34
Extra Example 1: Adding Decimals
5:32
Extra Example 2: How Much Money?
6:09
Extra Example 3: Subtracting Decimals
7:20
Extra Example 4: Adding Decimals
9:32
Multiplying Decimals

10m 30s

Intro
0:00
Multiply the Decimals
0:05
Methods for Multiplying Decimals
0:06
Example: 1.1 x 6
0:38
Extra Example 1: Multiplying Decimals
1:51
Extra Example 2: Work Money
2:49
Extra Example 3: Multiplying Decimals
5:45
Extra Example 4: Multiplying Decimals
7:46
Dividing Decimals

17m 49s

Intro
0:00
When Dividing Decimals
0:06
Methods for Dividing Decimals
0:07
Divisor and Dividend
0:37
Example: 0.2 Divided by 10
1:35
Extra Example 1 : Dividing Decimals
5:24
Extra Example 2: How Much Does Each CD Cost?
8:22
Extra Example 3: Dividing Decimals
10:59
Extra Example 4: Dividing Decimals
12:08
II. Number Relationships and Fractions
Prime Factorization

7m

Intro
0:00
Terms to Review
0:07
Prime vs. Composite
0:12
Factor
0:54
Product
1:15
Factor Tree
1:39
Example: Prime Factorization
2:01
Example: Prime Factorization
2:43
Extra Example 1: Prime Factorization
4:08
Extra Example 2: Prime Factorization
5:05
Extra Example 3: Prime Factorization
5:33
Extra Example 4: Prime Factorization
6:13
Greatest Common Factor

12m 47s

Intro
0:00
Terms to Review
0:05
Factor
0:07
Example: Factor of 20
0:18
Two Methods
0:59
Greatest Common Factor
1:00
Method 1: GCF of 15 and 30
1:37
Method 2: GCF of 15 and 30
2:58
Extra Example 1: Find the GCF of 6 and 18
5:16
Extra Example 2: Find the GCF of 36 and 27
7:43
Extra Example 3: Find the GCF of 6 and 18
9:18
Extra Example 4: Find the GCF of 54 and 36
10:30
Fraction Concepts and Simplest Form

10m 3s

Intro
0:00
Fraction Concept
0:10
Example: Birthday Cake
0:28
Example: Chocolate Bar
2:10
Simples Form
3:38
Example: Simplifying 4 out of 8
3:46
Extra Example 1: Graphically Show 4 out of 10
4:41
Extra Example 2: Finding Fraction Shown by Illustration
5:10
Extra Example 3: Simplest Form of 5 over 25
7:02
Extra Example 4: Simplest Form of 14 over 49
8:30
Least Common Multiple

14m 16s

Intro
0:00
Term to Review
0:06
Multiple
0:07
Example: Multiples of 4
0:15
Two Methods
0:41
Least Common Multiples
0:44
Method 1: LCM of 6 and 10
1:09
Method 2: LCM of 6 and 10
2:56
Extra Example 1: LCM of 12 and 15
5:09
Extra Example 2: LCM of 16 and 20
7:36
Extra Example 3 : LCM of 15 and 25
10:00
Extra Example 4 : LCM of 12 and 18
11:27
Comparing and Ordering Fractions

13m 10s

Intro
0:00
Terms Review
0:14
Greater Than
0:16
Less Than
0:40
Compare the Fractions
1:00
Example: Comparing 2/4 and 3/4
1:08
Example: Comparing 5/8 and 2/5
2:04
Extra Example 1: Compare the Fractions
3:28
Extra Example 2: Compare the Fractions
6:06
Extra Example 3: Compare the Fractions
8:01
Extra Example 4: Least to Greatest
9:37
Mixed Numbers and Improper Fractions

12m 49s

Intro
0:00
Fractions
0:10
Mixed Number
0:21
Proper Fraction
0:47
Improper Fraction
1:30
Switching Between
2:47
Mixed Number to Improper Fraction
2:53
Improper Fraction to Mixed Number
4:41
Examples: Switching Fractions
6:37
Extra Example 1: Mixed Number to Improper Fraction
8:57
Extra Example 2: Improper Fraction to Mixed Number
9:37
Extra Example 3: Improper Fraction to Mixed Number
10:21
Extra Example 4: Mixed Number to Improper Fraction
11:31
Connecting Decimals and Fractions

15m 1s

Intro
0:00
Examples: Decimals and Fractions
0:06
More Examples: Decimals and Fractions
2:48
Extra Example 1: Converting Decimal to Fraction
6:55
Extra Example 2: Converting Fraction to Decimal
8:45
Extra Example 3: Converting Decimal to Fraction
10:28
Extra Example 4: Converting Fraction to Decimal
11:42
III. Fractions and Their Operations
Adding and Subtracting Fractions with Same Denominators

5m 17s

Intro
0:00
Same Denominator
0:11
Numerator and Denominator
0:18
Example: 2/6 + 5/6
0:41
Extra Example 1: Add or Subtract the Fractions
2:02
Extra Example 2: Add or Subtract the Fractions
2:45
Extra Example 3: Add or Subtract the Fractions
3:17
Extra Example 4: Add or Subtract the Fractions
4:05
Adding and Subtracting Fractions with Different Denominators

23m 8s

Intro
0:00
Least Common Multiple
0:12
LCM of 6 and 4
0:31
From LCM to LCD
2:25
Example: Adding 1/6 with 3/4
3:12
Extra Example 1: Add or Subtract
6:23
Extra Example 2: Add or Subtract
9:49
Extra Example 3: Add or Subtract
14:54
Extra Example 4: Add or Subtract
18:14
Adding and Subtracting Mixed Numbers

19m 44s

Intro
0:00
Example
0:05
Adding Mixed Numbers
0:17
Extra Example 1: Adding Mixed Numbers
1:57
Extra Example 2: Subtracting Mixed Numbers
8:13
Extra Example 3: Adding Mixed Numbers
12:01
Extra Example 4: Subtracting Mixed Numbers
14:54
Multiplying Fractions and Mixed Numbers

21m 32s

Intro
0:00
Multiplying Fractions
0:07
Step 1: Change Mixed Numbers to Improper Fractions
0:08
Step2: Multiply the Numerators Together
0:56
Step3: Multiply the Denominators Together
1:03
Extra Example 1: Multiplying Fractions
1:37
Extra Example 2: Multiplying Fractions
6:39
Extra Example 3: Multiplying Fractions
10:20
Extra Example 4: Multiplying Fractions
13:47
Dividing Fractions and Mixed Numbers

18m

Intro
0:00
Dividing Fractions
0:09
Step 1: Change Mixed Numbers to Improper Fractions
0:15
Step 2: Flip the Second Fraction
0:27
Step 3: Multiply the Fractions
0:52
Extra Example 1: Dividing Fractions
1:23
Extra Example 2: Dividing Fractions
5:06
Extra Example 3: Dividing Fractions
9:34
Extra Example 4: Dividing Fractions
12:06
Distributive Property

11m 5s

Intro
0:00
Distributive Property
0:06
Methods of Distributive Property
0:07
Example: a(b)
0:35
Example: a(b+c)
0:49
Example: a(b+c+d)
1:22
Extra Example 1: Using Distributive Property
1:56
Extra Example 2: Using Distributive Property
4:36
Extra Example 3: Using Distributive Property
6:39
Extra Example 4: Using Distributive Property
8:19
Units of Measure

16m 36s

Intro
0:00
Length
0:05
Feet, Inches, Yard, and Mile
0:20
Millimeters, Centimeters, and Meters
0:43
Mass
2:57
Pounds, Ounces, and Tons
3:03
Grams and Kilograms
3:38
Liquid
4:11
Gallons, Quarts, Pints, and Cups
4:14
Extra Example 1: Converting Units
7:02
Extra Example 2: Converting Units
9:31
Extra Example 3: Converting Units
12:21
Extra Example 4: Converting Units
14:05
IV. Positive and Negative Numbers
Integers and the Number Line

13m 24s

Intro
0:00
What are Integers
0:06
Integers are all Whole Numbers and Their Opposites
0:09
Absolute Value
2:35
Extra Example 1: Compare the Integers
4:36
Extra Example 2: Writing Integers
9:24
Extra Example 3: Opposite Integer
10:38
Extra Example 4: Absolute Value
11:27
Adding Integers

16m 5s

Intro
0:00
Using a Number Line
0:04
Example: 4 + (-2)
0:14
Example: 5 + (-8)
1:50
How to Add Integers
3:00
Opposites Add to Zero
3:10
Adding Same Sign Numbers
3:37
Adding Opposite Signs Numbers
4:44
Extra Example 1: Add the Integers
8:21
Extra Example 2: Find the Sum
10:33
Extra Example 3: Find the Value
11:37
Extra Example 4: Add the Integers
13:10
Subtracting Integers

15m 25s

Intro
0:00
How to Subtract Integers
0:06
Two-dash Rule
0:16
Example: 3 - 5
0:44
Example: 3 - (-5)
1:12
Example: -3 - 5
1:39
Extra Example 1: Rewrite Subtraction to Addition
4:43
Extra Example 2: Find the Difference
7:59
Extra Example 3: Find the Difference
9:08
Extra Example 4: Evaluate
10:38
Multiplying Integers

7m 33s

Intro
0:00
When Multiplying Integers
0:05
If One Number is Negative
0:06
If Both Numbers are Negative
0:18
Examples: Multiplying Integers
0:53
Extra Example 1: Multiplying Integers
1:27
Extra Example 2: Multiplying Integers
2:43
Extra Example 3: Multiplying Integers
3:13
Extra Example 4: Multiplying Integers
3:51
Dividing Integers

6m 42s

Intro
0:00
When Dividing Integers
0:05
Rules for Dividing Integers
0:41
Extra Example 1: Dividing Integers
1:01
Extra Example 2: Dividing Integers
1:51
Extra Example 3: Dividing Integers
2:21
Extra Example 4: Dividing Integers
3:18
Integers and Order of Operations

11m 9s

Intro
0:00
Combining Operations
0:21
Solve Using the Order of Operations
0:22
Extra Example 1: Evaluate
1:18
Extra Example 2: Evaluate
4:20
Extra Example 3: Evaluate
6:33
Extra Example 4: Evaluate
8:13
V. Solving Equations
Writing Expressions

9m 15s

Intro
0:00
Operation as Words
0:05
Operation as Words
0:06
Extra Example 1: Write Each as an Expression
2:09
Extra Example 2: Write Each as an Expression
4:27
Extra Example 3: Write Each Expression Using Words
6:45
Writing Equations

18m 3s

Intro
0:00
Equation
0:05
Definition of Equation
0:06
Examples of Equation
0:58
Operations as Words
1:39
Operations as Words
1:40
Extra Example 1: Write Each as an Equation
3:07
Extra Example 2: Write Each as an Equation
6:19
Extra Example 3: Write Each as an Equation
10:08
Extra Example 4: Determine if the Equation is True or False
13:38
Solving Addition and Subtraction Equations

24m 53s

Intro
0:00
Solving Equations
0:08
inverse Operation of Addition and Subtraction
0:09
Extra Example 1: Solve Each Equation Using Mental Math
4:15
Extra Example 2: Use Inverse Operations to Solve Each Equation
5:44
Extra Example 3: Solve Each Equation
14:51
Extra Example 4: Translate Each to an Equation and Solve
19:57
Solving Multiplication Equation

19m 46s

Intro
0:00
Multiplication Equations
0:08
Inverse Operation of Multiplication
0:09
Extra Example 1: Use Mental Math to Solve Each Equation
3:54
Extra Example 2: Use Inverse Operations to Solve Each Equation
5:55
Extra Example 3: Is -2 a Solution of Each Equation?
12:48
Extra Example 4: Solve Each Equation
15:42
Solving Division Equation

17m 58s

Intro
0:00
Division Equations
0:05
Inverse Operation of Division
0:06
Extra Example 1: Use Mental Math to Solve Each Equation
0:39
Extra Example 2: Use Inverse Operations to Solve Each Equation
2:14
Extra Example 3: Is -6 a Solution of Each Equation?
9:53
Extra Example 4: Solve Each Equation
11:50
VI. Ratios and Proportions
Ratio

40m 21s

Intro
0:00
Ratio
0:05
Definition of Ratio
0:06
Examples of Ratio
0:18
Rate
2:19
Definition of Rate
2:20
Unit Rate
3:38
Example: $10 / 20 pieces
5:05
Converting Rates
6:46
Example: Converting Rates
6:47
Extra Example 1: Write in Simplest Form
16:22
Extra Example 2: Find the Ratio
20:53
Extra Example 3: Find the Unit Rate
22:56
Extra Example 4: Convert the Unit
26:34
Solving Proportions

17m 22s

Intro
0:00
Proportions
0:05
An Equality of Two Ratios
0:06
Cross Products
1:00
Extra Example 1: Find Two Equivalent Ratios for Each
3:21
Extra Example 2: Use Mental Math to Solve the Proportion
5:52
Extra Example 3: Tell Whether the Two Ratios Form a Proportion
8:21
Extra Example 4: Solve the Proportion
13:26
Writing Proportions

22m 1s

Intro
0:00
Writing Proportions
0:08
Introduction to Writing Proportions and Example
0:10
Extra Example 1: Write a Proportion and Solve
5:54
Extra Example 2: Write a Proportion and Solve
11:19
Extra Example 3: Write a Proportion for Word Problem
17:29
Similar Polygons

16m 31s

Intro
0:00
Similar Polygons
0:05
Definition of Similar Polygons
0:06
Corresponding Sides are Proportional
2:14
Extra Example 1: Write a Proportion and Find the Value of Similar Triangles
4:26
Extra Example 2: Write a Proportional to Find the Value of x
7:04
Extra Example 3: Write a Proportion for the Similar Polygons and Solve
9:04
Extra Example 4: Word Problem and Similar Polygons
11:03
Scale Drawings

13m 43s

Intro
0:00
Scale Drawing
0:05
Definition of a Scale Drawing
0:06
Example: Scale Drawings
1:00
Extra Example 1: Scale Drawing
4:50
Extra Example 2: Scale Drawing
7:02
Extra Example 3: Scale Drawing
9:34
Probability

11m 51s

Intro
0:00
Probability
0:05
Introduction to Probability
0:06
Example: Probability
1:22
Extra Example 1: What is the Probability of Landing on Orange?
3:26
Extra Example 2: What is the Probability of Rolling a 5?
5:02
Extra Example 3: What is the Probability that the Marble will be Red?
7:40
Extra Example 4: What is the Probability that the Student will be a Girl?
9:43
VII. Percents
Percents, Fractions, and Decimals

35m 5s

Intro
0:00
Percents
0:06
Changing Percent to a Fraction
0:07
Changing Percent to a Decimal
1:54
Fractions
4:17
Changing Fraction to Decimal
4:18
Changing Fraction to Percent
7:50
Decimals
10:10
Changing Decimal to Fraction
10:11
Changing Decimal to Percent
12:07
Extra Example 1: Write Each Percent as a Fraction in Simplest Form
13:29
Extra Example 2: Write Each as a Decimal
17:09
Extra Example 3: Write Each Fraction as a Percent
22:45
Extra Example 4: Complete the Table
29:17
Finding a Percent of a Number

28m 18s

Intro
0:00
Percent of a Number
0:06
Translate Sentence into an Equation
0:07
Example: 30% of 100 is What Number?
1:05
Extra Example 1: Finding a Percent of a Number
7:12
Extra Example 2: Finding a Percent of a Number
15:56
Extra Example 3: Finding a Percent of a Number
19:14
Extra Example 4: Finding a Percent of a Number
24:26
Solving Percent Problems

32m 31s

Intro
0:00
Solving Percent Problems
0:06
Translate the Sentence into an Equation
0:07
Extra Example 1: Solving Percent Problems
0:56
Extra Example 2: Solving Percent Problems
14:49
Extra Example 3: Solving Percent Problems
23:44
Simple Interest

27m 9s

Intro
0:00
Simple Interest
0:05
Principal
0:06
Interest & Interest Rate
0:41
Simple Interest
1:43
Simple Interest Formula
2:23
Simple Interest Formula: I = prt
2:24
Extra Example 1: Finding Simple Interest
3:53
Extra Example 2: Finding Simple Interest
8:08
Extra Example 3: Finding Simple Interest
12:02
Extra Example 4: Finding Simple Interest
17:46
Discount and Sales Tax

17m 15s

Intro
0:00
Discount
0:19
Discount
0:20
Sale Price
1:22
Sales Tax
2:24
Sales Tax
2:25
Total Due
2:59
Extra Example 1: Finding the Discount
3:43
Extra Example 2: Finding the Sale Price
6:28
Extra Example 3: Finding the Sale Tax
11:14
Extra Example 4: Finding the Total Due
14:08
VIII. Geometry in a Plane
Intersecting Lines and Angle Measures

24m 17s

Intro
0:00
Intersecting Lines
0:07
Properties of Lines
0:08
When Two Lines Cross Each Other
1:55
Angles
2:56
Properties of Angles: Sides, Vertex, and Measure
2:57
Classifying Angles
7:18
Acute Angle
7:19
Right Angle
7:54
Obtuse Angle
8:03
Angle Relationships
8:56
Vertical Angles
8:57
Adjacent Angles
10:38
Complementary Angles
11:52
Supplementary Angles
12:54
Extra Example 1: Lines
16:00
Extra Example 2: Angles
18:22
Extra Example 3: Angle Relationships
20:05
Extra Example 4: Name the Measure of Angles
21:11
Angles of a Triangle

13m 35s

Intro
0:00
Angles of a Triangle
0:05
All Triangles Have Three Angles
0:06
Measure of Angles
2:16
Extra Example 1: Find the Missing Angle Measure
5:39
Extra Example 2: Angles of a Triangle
7:18
Extra Example 3: Angles of a Triangle
9:24
Classifying Triangles

15m 10s

Intro
0:00
Types of Triangles by Angles
0:05
Acute Triangle
0:06
Right Triangle
1:14
Obtuse Triangle
2:22
Classifying Triangles by Sides
4:18
Equilateral Triangle
4:20
Isosceles Triangle
5:21
Scalene Triangle
5:53
Extra Example 1: Classify the Triangle by Its Angles and Sides
6:34
Extra Example 2: Sketch the Figures
8:10
Extra Example 3: Classify the Triangle by Its Angles and Sides
9:55
Extra Example 4: Classify the Triangle by Its Angles and Sides
11:35
Quadrilaterals

17m 41s

Intro
0:00
Quadrilaterals
0:05
Definition of Quadrilaterals
0:06
Parallelogram
0:45
Rectangle
2:28
Rhombus
3:13
Square
3:53
Trapezoid
4:38
Parallelograms
5:33
Parallelogram, Rectangle, Rhombus, Trapezoid, and Square
5:35
Extra Example 1: Give the Most Exact Name for the Figure
11:37
Extra Example 2: Fill in the Blanks
13:31
Extra Example 3: Complete Each Statement with Always, Sometimes, or Never
14:37
Area of a Parallelogram

12m 44s

Intro
0:00
Area
0:06
Definition of Area
0:07
Area of a Parallelogram
2:00
Area of a Parallelogram
2:01
Extra Example 1: Find the Area of the Rectangle
4:30
Extra Example 2: Find the Area of the Parallelogram
5:29
Extra Example 3: Find the Area of the Parallelogram
7:22
Extra Example 4: Find the Area of the Shaded Region
8:55
Area of a Triangle

11m 29s

Intro
0:00
Area of a Triangle
0:05
Area of a Triangle: Equation and Example
0:06
Extra Example 1: Find the Area of the Triangles
1:31
Extra Example 2: Find the Area of the Figure
4:09
Extra Example 3: Find the Area of the Shaded Region
7:45
Circumference of a Circle

15m 4s

Intro
0:00
Segments in Circles
0:05
Radius
0:06
Diameter
1:08
Chord
1:49
Circumference
2:53
Circumference of a Circle
2:54
Extra Example 1: Name the Given Parts of the Circle
6:26
Extra Example 2: Find the Circumference of the Circle
7:54
Extra Example 3: Find the Circumference of Each Circle with the Given Measure
11:04
Area of a Circle

14m 43s

Intro
0:00
Area of a Circle
0:05
Area of a Circle: Equation and Example
0:06
Extra Example 1: Find the Area of the Circle
2:17
Extra Example 2: Find the Area of the Circle
5:47
Extra Example 3: Find the Area of the Shaded Region
9:24
XI. Geometry in Space
Prisms and Cylinders

21m 49s

Intro
0:00
Prisms
0:06
Polyhedron
0:07
Regular Prism, Bases, and Lateral Faces
1:44
Cylinders
9:37
Bases and Altitude
9:38
Extra Example 1: Classify Each Prism by the Shape of Its Bases
11:16
Extra Example 2: Name Two Different Edges, Faces, and Vertices of the Prism
15:44
Extra Example 3: Name the Solid of Each Object
17:58
Extra Example 4: Write True or False for Each Statement
19:47
Volume of a Rectangular Prism

8m 59s

Intro
0:00
Volume of a Rectangular Prism
0:06
Volume of a Rectangular Prism: Formula
0:07
Volume of a Rectangular Prism: Example
1:46
Extra Example 1: Find the Volume of the Rectangular Prism
3:39
Extra Example 2: Find the Volume of the Cube
5:00
Extra Example 3: Find the Volume of the Solid
5:56
Volume of a Triangular Prism

16m 15s

Intro
0:00
Volume of a Triangular Prism
0:06
Volume of a Triangular Prism: Formula
0:07
Extra Example 1: Find the Volume of the Triangular Prism
2:42
Extra Example 2: Find the Volume of the Triangular Prism
7:21
Extra Example 3: Find the Volume of the Solid
10:38
Volume of a Cylinder

15m 55s

Intro
0:00
Volume of a Cylinder
0:05
Volume of a Cylinder: Formula
0:06
Extra Example 1: Find the Volume of the Cylinder
1:52
Extra Example 2: Find the Volume of the Cylinder
7:38
Extra Example 3: Find the Volume of the Cylinder
11:25
Surface Area of a Prism

23m 28s

Intro
0:00
Surface Area of a Prism
0:06
Surface Area of a Prism
0:07
Lateral Area of a Prism
2:12
Lateral Area of a Prism
2:13
Extra Example 1: Find the Surface Area of the Rectangular Prism
7:08
Extra Example 2: Find the Lateral Area and the Surface Area of the Cube
12:05
Extra Example 3: Find the Surface Area of the Triangular Prism
17:13
Surface Area of a Cylinder

27m 41s

Intro
0:00
Surface Area of a Cylinder
0:06
Introduction to Surface Area of a Cylinder
0:07
Surface Area of a Cylinder
1:33
Formula
1:34
Extra Example 1: Find the Surface Area of the Cylinder
5:51
Extra Example 2: Find the Surface Area of the Cylinder
13:51
Extra Example 3: Find the Surface Area of the Cylinder
20:57
X. Data Analysis and Statistics
Measures of Central Tendency

24m 32s

Intro
0:00
Measures of Central Tendency
0:06
Mean
1:17
Median
2:42
Mode
5:41
Extra Example 1: Find the Mean, Median, and Mode for the Following Set of Data
6:24
Extra Example 2: Find the Mean, Median, and Mode for the Following Set of Data
11:14
Extra Example 3: Find the Mean, Median, and Mode for the Following Set of Data
15:13
Extra Example 4: Find the Three Measures of the Central Tendency
19:12
Histograms

19m 43s

Intro
0:00
Histograms
0:05
Definition and Example
0:06
Extra Example 1: Draw a Histogram for the Frequency Table
6:14
Extra Example 2: Create a Histogram of the Data
8:48
Extra Example 3: Create a Histogram of the Following Test Scores
14:17
Box-and-Whisker Plot

17m 54s

Intro
0:00
Box-and-Whisker Plot
0:05
Median, Lower & Upper Quartile, Lower & Upper Extreme
0:06
Extra Example 1: Name the Median, Lower & Upper Quartile, Lower & Upper Extreme
6:04
Extra Example 2: Draw a Box-and-Whisker Plot Given the Information
7:35
Extra Example 3: Find the Median, Lower & Upper Quartile, Lower & Upper Extreme
9:31
Extra Example 4: Draw a Box-and-Whiskers Plots for the Set of Data
12:50
Stem-and-Leaf Plots

17m 42s

Intro
0:00
Stem-and-Leaf Plots
0:05
Stem-and-Leaf Plots
0:06
Extra Example 1: Use the Data to Create a Stem-and-Leaf Plot
2:28
Extra Example 2: List All the Numbers in the Stem-and-Leaf Plot in Order From Least to Greatest
7:02
Extra Example 3: Create a Stem-and-Leaf Plot of the Data & Find the Median and the Mode.
8:59
The Coordinate Plane

19m 59s

Intro
0:00
The Coordinate System
0:05
The Coordinate Plane
0:06
Quadrants, Origin, and Ordered Pair
0:50
The Coordinate Plane
7:02
Write the Coordinates for Points A, B, and C
7:03
Extra Example 1: Graph Each Point on the Coordinate Plane
9:03
Extra Example 2: Write the Coordinate and Quadrant for Each Point
11:05
Extra Example 3: Name Two Points From Each of the Four Quadrants
13:13
Extra Example 4: Graph Each Point on the Same Coordinate Plane
17:47
XI. Probability and Discrete Mathematics
Organizing Possible Outcomes

15m 35s

Intro
0:00
Compound Events
0:08
Compound Events
0:09
Fundamental Counting Principle
3:35
Extra Example 1: Create a List of All the Possible Outcomes
4:47
Extra Example 2: Create a Tree Diagram For All the Possible Outcomes
6:34
Extra Example 3: Create a Tree Diagram For All the Possible Outcomes
10:00
Extra Example 4: Fundamental Counting Principle
12:41
Independent and Dependent Events

35m 19s

Intro
0:00
Independent Events
0:11
Definition
0:12
Example 1: Independent Event
1:45
Example 2: Two Independent Events
4:48
Dependent Events
9:09
Definition
9:10
Example: Dependent Events
10:10
Extra Example 1: Determine If the Two Events are Independent or Dependent Events
13:38
Extra Example 2: Find the Probability of Each Pair of Events
18:11
Extra Example 3: Use the Spinner to Find Each Probability
21:42
Extra Example 4: Find the Probability of Each Pair of Events
25:49
Disjoint Events

12m 13s

Intro
0:00
Disjoint Events
0:06
Definition and Example
0:07
Extra Example 1: Disjoint & Not Disjoint Events
3:08
Extra Example 2: Disjoint & Not Disjoint Events
4:23
Extra Example 3: Independent, Dependent, and Disjoint Events
6:30
Probability of an Event Not Occurring

20m 5s

Intro
0:00
Event Not Occurring
0:07
Formula and Example
0:08
Extra Example 1: Use the Spinner to Find Each Probability
7:24
Extra Example 2: Probability of Event Not Occurring
11:21
Extra Example 3: Probability of Event Not Occurring
15:51
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Lecture Comments (6)

1 answer

Last reply by: Maryanne Stevens
Fri Jan 29, 2016 6:38 PM

Post by Maryanne Stevens on January 29, 2016

Hello,
I think the last problem you forgot to multiply by 10 in regards to finding LA. You only did (2X3.14X6) which is 37.68, however you didn't multiply this by 10, which should be 3,768 inches square, then add the area of the two bases(circles in this case). I paused your video and completed the problem. ,y answer was 3,768 inches square + 2(113.04)inches = 3,994.08 inches square.
Am I right, or are you right?
Thank you

1 answer

Last reply by: Khanh Nguyen
Sat Jul 25, 2015 12:37 AM

Post by Milan Ray on April 15, 2014

What are the circles for!

0 answers

Post by Daniel G Swedlund on August 31, 2013

I think the latin number for 9 = IX. While XI = 11.

0 answers

Post by Arpana Duggal on July 2, 2012

this chapter isnt 11 its 9!

Related Articles:

Surface Area of a Cylinder

Related Links

  • Surface area of a cylinder: The sum of the lateral area and the two bases
  • Surface area = Lateral area + 2(Area of the circle)

Surface Area of a Cylinder

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Surface Area of a Cylinder 0:06
    • Introduction to Surface Area of a Cylinder
  • Surface Area of a Cylinder 1:33
    • Formula
  • Extra Example 1: Find the Surface Area of the Cylinder 5:51
  • Extra Example 2: Find the Surface Area of the Cylinder 13:51
  • Extra Example 3: Find the Surface Area of the Cylinder 20:57

Transcription: Surface Area of a Cylinder

Welcome back to Educator.com.0000

For the next lesson, we are going to go over the surface area of a cylinder.0002

Remember surface area is the area of all the sides of the solid.0007

For the cylinder, we are going to find the area of the top base, the bottom base,0013

and then the lateral area which is the rectangle which makes up the side of the cylinder.0023

Imagine if this is a can of soup.0035

If you were to rip off the label, the label that wraps around the can, this is a cylinder.0041

If you were to cut it and rip off the label, it becomes a rectangle.0053

Here the lateral area, meaning this side that does not include the bases,0061

if you cut it and open it up, then it becomes a rectangle.0071

The lateral area for the cylinder is the rectangle that makes up the side of the cylinder.0081

Then we have of course the two bases which are circles.0089

Surface area is the lateral area plus the two bases, the two circles.0095

To find the lateral area, if this is where we cut, then there is the cut right there.0105

We need to find the measure of this length and width0121

to be able to find the area of this lateral area, this rectangle.0126

Here we know that this wraps around this base.0131

All of this here becomes this here.0137

When you are given this cylinder, to find this measure, to find that length,0145

we have to be able to find the length of this circle right here.0151

If we had a prism, that would be considered the perimeter of the base.0158

But because it is a circle, that is called circumference.0162

To find the circumference of a circle, it is going to be 2πr.0167

This is 2πr; circumference, all of this; circumference equals 2πr.0175

π is 3.14; there is the r; there is the radius.0188

Once you find that, that will be the length of this right there.0195

We know this would be the height.0199

That would just be the height of the cylinder.0202

To find the area of a circle, because we have to find the area of this whole thing.0206

This whole thing is this whole thing right here.0210

The area of a circle is πr2; a few things to look at here.0215

We have circumference to help us find the length of this rectangle, the lateral area.0223

We have the area of a circle because that is the area of the base.0231

Be careful here not to get confused with volume.0236

Surface area and volume are very different things.0239

Surface area, we are just finding the space of the outside of the cylinder.0242

Whereas volume measures everything inside, how much space it is covering on the inside.0249

Surface area will be the lateral area; lateral area is this times this.0257

It is circumference times the height; or I can just say 2πr times h.0270

That is going to give me the lateral area, all of this here.0282

Plus... now I have to find the area of my bases.0286

Plus, since I have two bases, 2 times πr2.0291

The surface area SA is going to be all this here.0301

Try not to let this confuse you; surface area is just very simple.0306

You are just finding all the space on the outside.0311

Just this right here, the area of this rectangle, plus the area of the circle which is the top.0319

Plus the area of this bottom circle which is the bottom.0329

It is just area of the rectangle plus the two bases of the cylinder.0333

That is the surface area.0339

As long as you are comfortable, you know the circumference of a circle,0341

you know how to find the area of a circle, you are fine with surface area.0345

Let's do a few examples.0351

Again try not to get confused with the formula for volume.0354

The volume is the area of a circle πr2 times the height of the cylinder.0359

That is the volume.0370

For surface area, we are just going to take it one step at a time0371

and find the lateral area, find the area of that label that wraps around the can.0377

Then add it to our bases, the area of the bases.0383

Surface area, we are going to do lateral area which is that label0388

plus the area of the base which is a circle, πr2 since it is a circle,0394

and multiply that by 2 because we have two of those bases.0401

Again remember a lateral area, we are finding the rectangle; that label, rectangle.0407

If we cut it here, then it is as if we are cutting it here.0416

We need to find this measure here which would be this measure there which is the circumference.0425

The circumference is 2πr; that is 2 times 3.14 times... the radius is 4.0433

2 times 3.14 is... 2 times 1 is 2; this is 6.0453

I have two numbers behind decimal points; that will be 6.28.0467

Times 4; this is 32; that is 8, 9, 10, 11; 24, 25.0471

Again two numbers; it is 25.12.0484

Easier way, you can just multiply this number with this number first.0488

That is 8; then you can multiply that 8 to 3.14.0494

Here our circumference is 25.12; this is 25.12.0500

That is the length of this side right here; this height is 6.0506

The lateral area... I am going to write that in here.0516

Lateral area is 25.12 times 6; lateral area.0521

25.12 times the 6; this is 12.0542

6 times 1 is 6; plus 1 is 7.0551

5 times 6 is 30; 6 times 2 is 12; plus 3 is 15.0554

How many numbers do I have behind decimal points?--I have two.0566

That means I have to place two numbers behind the decimal point here in my answer.0570

25.12 times 6 is 150.72; that is only this part right here.0576

Plus... now I have to find the area of my base, πr2, all of this right here.0589

πr2; the area of the base is πr2.0603

That is 3.14 times the radius which is 42.0613

Remember that I have to square this first; 4 times 4 is 16.0620

3.14 times 16; 4 times 6 is 24.0627

6 times 1 is 6; plus 2 is 8; 6 times 3 is 18.0640

Leave this space alone; 1 times 4 is 4; this is 1; this is 3.0647

I am going to add them up; 4, 12, 10, 5.0653

I have a total of two spaces behind decimal points.0661

I have to put that decimal point right there; it becomes 50.24.0666

The area of this base right here πr2 is 50.24.0671

I just place that right here, that number, 50.24.0684

Since I have two of them, I have to multiply that by 2.0692

If you want, you can just do 50.24 plus 50.24; times 2.0699

4 times 2 is 8; this is 4.0; that is 10.0712

All this lateral area plus 100.48 is surface area; add these two numbers together.0722

Remember when you add decimals, you have to line up the decimal point.0742

2 plus 8 is 10; 7 plus 4 is 11; plus the 1 is 12.0749

1, 5, and 2; decimal point, just bring it straight down.0760

My surface area is 251.20; my units, centimeters; it is area so it is squared.0766

I know this was a lot of work; this was a lot.0780

But all we did is find the area of that label.0783

Remember that rectangle that wraps around the can.0787

We are going to find the area of that; it is just a rectangle.0791

You are just finding 2πr because that is this side right here; times the 6.0794

If you want, instead of using this whole formula here, you can just maybe draw out the rectangle.0802

Draw your two bases, your circles; find the area of each one.0810

Then just add them together; that is all we did here.0816

This is just rectangle plus the base times 2; that is surface area.0819

Let's do a couple more examples; find the surface area of the cylinder.0829

For this one, let's draw out our net.0836

Meaning I am going to draw out my rectangle which is that label that wraps around the can.0843

Then my two circles.0851

First let's find the area of that rectangle; this I know is 20 meters.0859

Then to find this measure here, that is just from here going all the way around.0871

That is remember circumference; this is going to be 2πr.0879

2; π is 3.14; r, my radius is not given; I have my diameter instead.0889

The diameter is remember from here all the way to here is 12.0898

My radius is half of that; r is 6; it is times 6.0903

To find this, I can just multiply these two first.0912

2 times 6 is 12; 12 times 3.14; 3.14 times 12.0918

This is 8, 2, 6; leave the space alone; 1 times 4 is 4.0930

That is 1; that is 3; now we add; 8, 6, 7, 3.0940

I have two numbers total behind decimal points.0950

Place the decimal point in front of two numbers.0953

This side right here, my circumference, is 37.68.0957

To find the area of this, just multiply this number times that number.0966

It is 20 times 37.68; 37.68 times 20.0971

If you want, you can drop the 0 and just multiply this number by the 2.0986

But you have to remember that in your answer, after you multiply it by 2,0994

you have to place a 0 at the end of that.0997

That is just a little faster way to do it.1000

Or I can just say that this is 0.1004

Then instead of placing... because everything times this is all 0.1008

Instead of writing all these 0s, I can just go ahead and start multiplying this next number, the 2.1011

2 times 8 is 16; this is 12, 13, 14, 15; 6, 7.1018

Two numbers behind decimal points; right there.1031

The area of this is 753.6 meters squared.1037

That is the area of this rectangle there.1054

Now let's find the area of the base, this right here, the circle.1058

That will be πr2; π is 3.14; radius is 62.1065

Again exponent first; that is 3.14 times 36.1080

4 times 6 is 24; 6 times 1 is 6; plus 2.1096

6 times 3 is 18; put a 0 there; 3 times 4 is 12.1102

3 times 1 is 3; plus the 1; 4; 9.1113

Add them; 4; 10; 12, 13; 9, 10, 11; two numbers there.1120

My area of this circle is 113.04 meters squared; that is the area of that.1134

The area of this is also 113.04.1150

Now all I have to do to find the surface area is add them together.1158

753.6 or 60... remember if this is a 0 that is behind the decimal point1163

and at the end of a number, you can just drop it.1175

Plus my circles; 113.04 plus 113.04.1180

Let's go ahead and just add them; line them up.1196

753.60 with this one, 113.04 and 113.04.1199

Make sure when you add decimals, the decimal points all line up.1213

The decimal point in the answer is just going to go straight down.1218

This is 8; 6 plus 0 plus 0; 6.1222

3, 6, 9; 5, 6, 7; 7, 8, 9.1228

Our surface area is 979.68 meters squared for area.1238

Third example, we have a cylinder that has a radius of 6 inches and a height of 10 inches.1260

Draw a net for the cylinder and find the surface area.1267

Cylinder, there is my cylinder there.1274

My radius is 6 inches; my height is 10 inches.1283

The net is going to be rectangle for the lateral area and then my two circles, my bases.1294

The surface area is going to be this plus this plus that.1310

Remember to find the length here, that is going to be1319

from here all the way wrapping around which is the circumference.1326

That is 2πr; the radius is 6.1333

This is going to be 2 times 3.14 times 6.1339

I can go ahead and multiply this 2 and the 6 together.1347

That is 12; times the 3.14; that is going to give this length right there.1350

3.14 times 12; 8; 2; 6; 1 times 4.1359

Leave this space alone; put a 0 there; 4, 1, and 3.1369

Add them; it is 8; this is 6; 6, 7, 3.1376

I have two numbers behind decimal points here.1385

I am going to place the decimal point right there in front of two numbers.1388

My circumference here, this length is going to be 37.68; my height is 10.1397

To find the area of this rectangle, I have to multiply this times this, length times the width.1409

Here if you just multiply by 10, all I have to do is1418

take the decimal point and move it over to the right one space.1424

The area of this rectangle is going to be 376.8.1429

It went from in front of the 6 to behind the 6; one space.1436

Then plus... I have to find the area of that circle.1443

The area of a circle is πr2.1448

π is 3.14; the radius is 6; 3.14 times 62.1453

Remember we have to take care of this exponent first.1465

6 times 6 is 36; it is 3.14 times 36.1468

This is 24; this is 6; add the 2; 8; this is 18.1479

Leave the space alone; put a 0.1488

3 times 4 is 12; 3 times 1 is 3; plus 1 is 4.1490

3 times 3 is 9; 4; now we are adding.1496

8 plus 2 is 10; this is 12, 13; 9, 10, 11.1503

Two numbers behind decimal points; it is going to go right there.1512

The area of this circle is 113.04.1517

This is the same circle, same area; this is 113.04 also.1526

To find the surface area, I take this which is called my lateral area.1533

Lateral area plus area of my base; then add another base because I have two of them.1540

If you want, you can just take this and multiply it by 2 since we have two of them.1553

I just have to add this all up.1558

Remember when we add decimals together, we have to line up the decimal point.1563

Decimal point has to go right there; that is 04; again 113.04.1569

I am missing a number right here; I can just place a 0.1581

Whenever you have a number behind the decimal point1585

and at the end of a number, you can add as many 0s as you need.1590

We are going to add this.1595

4 plus 4 is 8; 8 plus 0 plus 0 is 8 point...1597

6 plus 3 is 9; plus 3 is 12; 7, 8, 9, 10.1605

1 there; 0 there; 3, 4, 5, 6.1614

My surface area when I add the lateral area... here is my base and my other base.1619

When you add lateral area plus the base plus the base,1631

we are going to get our surface area which is 602.88.1635

Our units is inches; area is always squared.1642

That is the surface area of this cylinder.1649

That is it for this lesson; thank you for watching Educator.com.1655

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