Math 10C

Chapter 2 Surface Area and Volume

Lesson 2.3 Volume

Focus

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

TEXT Page 80

Read/Work through the  Focus  section at the top of page 80 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 Page 80

Unless you , by coincidence, happen to have some conical paper cups handy,  AS WELL AS a cylinder that has the exact same height and diameter as your paper cup,  then this is NOT going to be useful.

(see below for a video that demonstrates EXACTLY what the investigate is trying to show.

Not quite as good as doing it yourself, but since the materials required are not readily available, this is a reasonable way to get the same information)

Watch

The video you can link to below (from YouTube) shows exactly what this investigation is trying to demonstrate.
Sadly,  the presenter does the algebra FIRST and only then does the demonstration.
It's still a good video, and if you only want to watch the "good stuff",  skip to 2:50 in the video.

Video Tutorial

https://youtu.be/yfuHUBDH2T0

Link the Ideas

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

TEXT Page 81

Read/Work through the  Link the Ideas  section on Page 81 in your textbook.

It will be important to know if your teacher will expect you to memorize these formulas, or if you will have access to them on a formula page.

It would be nice to have an understanding of WHERE these formulas come from, WHY they work, etc. , but...  in some cases it’s not possible to do this without calculus.

I would expect for most students they will focus on USING the formulas, knowing WHEN and HOW to apply them.

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 Volume of a Right Cylinder and a Right Cone

TEXT Page 82

Work through Example 1 on Page 82 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 2  Calculate the Volume of a Right Pyramid

TEXT Page 83

Work through Example 2 on Page 83  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 an Unknown Dimension When Given a Volume

TEXT Page 84

Work through Example 3 on Page 84 in your textbook.

Watch

Video Tutorial

Using your TI calculator to take cube roots

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  Finding the Volume of Composite Figures

TEXT Pages 84 - 85

Work through Example 4 on Pages 84 - 85 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!

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

For all these problems, I am assuming the use of a formula page, probably the standard procedure for most teachers.  Your page should hopefully have similar information to the page I am using,  so hopefully  my video content will be helpful!

Practice Problem 14,   I got the answer in the back of the book, (by some trial and error) and DID make a video, but I have no idea how this question would work... Let me know if you figure it out....!

Practice Problem 15,  some information on cell phones in THIS You Tube Video.  Amazing to see the differences between then and now.  But... a trivial question.....

Practice Problem 18,  I spent some time working on this,  but could not do the problem.   I am probably missing something obvious, but just can’t see it.  Would welcome any feedback on this one!

Practice Problem 20,  a discussion/investigation that will depend on the object you choose.   No video was created.

Practice Problem 21,  a discussion/investigation that will depend on the object you choose.   No video was created.

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 13", "Question 14", "Question 15"}, {"Question 16", "Question 17",  , "Question 19",  }})