Math 10C

Chapter 2 Surface Area and Volume

Lesson 2.2  Surface Area

Focus

The FOCUS section introduces the main concept that will be covered in the lesson.

TEXT Page 66

Read/Work through the  Focus  section at the top of page 66 in  your textbook.

Investigate

Investigate an idea or problem, with a partner if possible.
The investigation provides the background for the ideas presented in the lesson.

TEXT Pages 66 - 67

This is intended to be a group activity,  and you are asked to answer questions based on the material in this lesson, which you haven’t done yet!

Your teacher may want you to DO this investigation, in which case you can follow the instructions they will give to you.

Otherwise,  I believe it would be appropriate to skip this section and go to the Link the Ideas section where all these ideas will be actually presented to you.

Link the Ideas

Link the Ideas summarizes the math in the lesson.
A presentation of ideas connected to the lesson focus.

TEXT Pages 68 - 69

Read/Work through the  Link the Ideas  section on Pages 68 - 69 in your textbook.

Deriving the formulas in this section is not easy.
(In fact, formulas for things that are NOT right prisms USUALLY involve Calculus to be able to derive them)

As important as it is to UNDERSTAND these ideas,  most students will like simply want to know WHEN to use the given formulas, and HOW to apply them.

If you don’t read these pages, be SURE to read the information in the sidebars  (on the sides of the pages)

Watch   Surface area of a cone

A great YouTube video showing the construction of a cone from a net.  (using paper, scissors, glue, etc.)

LINK
https://youtu.be/oH8eu59HOCY

THE BIG IDEA here is that the SURFACE AREA would be how much paper it takes to create the cone.

Or... how much ink would it take to COLOR the surface of the cone.

CONTRAST this with VOLUME,  which would be how much SPACE in three dimensions the cone takes up.

Or, related,  the CAPACITY of the cone, which is how much STUFF the cone could hold if you filled it with water or rice, etc.

As you work through this unit,  you should constantly be thinking and contrasting the difference between surface area and volume/capacity.

Slant height of a cone

This demonstration illustrates the very important difference between the SLANT HEIGHT of a cone,  and the HEIGHT of a cone.  
(height is sometimes called vertical height or altitude)

LINK
https://www.mathopenref.com/coneslantheight.html

(and a pyramid works the same way, having both a slant height and a height)

Examples

Examples will give you TOOLS for solving problems, and also show you that there may be different ways to approach a question.

Example 1  Calculate the Surface Area of a Right Cone

TEXT Page 69

Work through Example 1 on Page 69 in your textbook.

Watch

Video comments

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Example 2  Calculate the Surface Area of a Right Pyramid

TEXT Page 70

Work through Example 2 on Page 70  in your textbook.

Watch

Video Tutorial

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Example 3  Calculate the Surface Area of a Sphere

TEXT Page 71

Work through Example 3 on Page 71 in your textbook.

Watch

Video Tutorial

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Example 4  Determine a Dimension When the Surface Area is Known

TEXT Page 71

Work through Example 4 on Page 71 in your textbook.

Watch

Video Tutorial

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Example 5  Visualize and Find Surface Areas of Composite Objects

TEXT Pages 72 - 73

Work through Example 5 on Pages 72 - 73 in your textbook.

Watch

Video Tutorial

Your Turn

YOUR TURN gives YOU the chance to try to do a problem ON YOUR OWN,  using the example as  a model.

Use the Video Tutorial for help, or to check your work, BUT... you should do your best to do this question ON YOUR OWN FIRST!

Video Tutorial

Key Ideas

Key Ideas summarizes the main new concepts of the lesson.

•	Carefully read through each of the bullet points in this section.

•	If you are unclear about any of these ideas,  ASK YOUR TEACHER FOR HELP!

It will be super IMPORTANT for you to hear from your teacher whether you need to memorize these formulas,  or if they will be PROVIDED on a formula sheet for you to simply look up and use.

Once I find out which formula page you will be using in this class,  I will make a video explaining what the parts of the formulae are.

For the cone and the sphere,  you pretty much have to accept what you see and use it,  since it's very difficult to PROVE that those formulas work.

But for the pyramid , cylinder, and right prism,  it's completely LOGICAL, and whenever you CAN understand a formula, it's way better.

You will do much better if you are using something that you understand,  instead of just trying to plug in numbers and hoping for the best!

Check Your Understanding    (Practice Problems)

Doing Practice Problems

Practice problems reinforce the math presented in this lesson.

•	Work through the practice problems for this lesson.
	These problems are for practice, you don’t need to hand them in!
	(your teacher may assign specific questions for you to complete)

•	Use the answers in the back of the book to CHECK YOUR WORK!

•	If you make a mistake, TRY TO FIX IT!

•	If you need help or want more information, view the video solutions provided.

•	If you still need more help,  CONTACT YOUR TEACHER!

Types of Practice Problems

Practice questions require basic understanding of the ideas of the  lesson.

Apply questions will require you to dig deeper for a solution.

Extend questions offer enrichment and extension.

Create Connections questions connect the math to everyday contexts.

Mini Lab (optional)  your teacher may or may not have you do these.

Notes

Question 13, .... just plug into the formula, one step problem... no video required...?

Question 18, asks you to create a spreadsheet,  a super useful thing to be able to do.  
Not sure if your teacher will expect you to be able to do this.  
But... the result of this investigation is one of the FUNDAMENTAL ideas that connects measurements of length, area, and volume.  
So,  I think it’s a good video to watch....

Question 19, asks you to create your own composite object.  If you do, great!   You can send your work to your teacher to have them check your calculations.

Question 20, in your own words...  The back of the book gives a reasonable answer (in their words...)

Video Solution Links

Check your work for every problem you do!
If you make a mistake,  try to fix it!
Use the video solutions for more information.
If a problem still doesn’t make sense, ASK YOUR TEACHER FOR HELP!

({{"Question 1", "Question 2", "Question 3", "Question 4", "Question 5"}, {"Question 6", "Question 7", "Question 8", "Question 9", "Question 10"}, {"Question 11", "Question 12",  , "Question 14", "Question 15"}, {"Question 16", "Question 17", "Question 18",  ,  }})