Math 20-3

Chapter 3 Surface Area, Volume, and Capacity

Lesson 3.2  Surface area of Pyramids, Cylinders, Spheres, & Cones

Formula page

I expect that you will be able to use a formula page for this class,  but that will be determined by your teacher.

Your teacher may have a formula page they expect you to use.

Below is a link to the formula page I will use (at least for now!) when I’m doing questions for this class.

This may change, depending on feedback from your teacher.

I encourage you to download this page and print it so you have it handy when you are doing math.

LINK
https://drive.google.com/file/d/1RP1ih45uxqdYk0HP8_fpw2zrb4Z-K6iM/view?usp=sharing

Math on the Job  Page 127

Read/Work through this section of your textbook and try to answer the questions.
These ideas will be developed in the examples

Explore the Math  Pages 127 - 128

Read/Work through this section of your textbook.
These ideas will be developed in the examples

For many of these shapes,  you will be using the formulas on your formula page to calculate surface area.
It’s always good to know WHY, but for some common shapes (eg.  a sphere),  it’s difficult to give an easy why.
So the big focus here is USING formulas to find surface areas.

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.

Cylinders

Video Tutorial   (cutting up a “tube” to illustrate surface area)

A website that illustrates the surface area of a cylinder.  LINK

Below is a net for a cylinder.  Note that in order for the net to work,  the circles MUST be on opposite sides of the rectangle.

A "net" for a sphere

Shown above is how you create a "net" for a sphere.

If you join the edges of these pieces,  you can form a sphere.

These pieces are called "gores"

Sometimes you will see a map of the earth formed using gores.

This gives an accurate representation of the relative positions and areas and shapes of things on the earth, but it's not a very useful kind of map since the pieces would rip and get lost easily,and the map has all kinds of gaps....

However.... there is no easy way to calculate the area of these gores.

For this class, you will be using the given  formula on your formula page to find the surface area of a sphere.

Surface area of a sphere of radius r = 4 π (r^2)

Discuss the Ideas  Page 128

Read/Work through this section of your textbook.
These ideas will be developed in the examples

Video Tutorial

Example 1  Page 129

Read the example problem and try to answer the question YOURSELF if you can.
Use the textbook solution or the Video Tutorial if you need help.

Video Tutorial

Example 2  Page 130

Read the example problem and try to answer the question YOURSELF if you can.
Use the textbook solution or the Video Tutorial if you need help.

Video Tutorial

Example 3  Page 132

Read the example problem and try to answer the question YOURSELF if you can.
Use the textbook solution or the Video Tutorial if you need help.

Video Tutorial

Example 4  Pages 132 - 133

Read the example problem and try to answer the question YOURSELF if you can.
Use the textbook solution or the Video Tutorial if you need help.

Video Tutorial

Mental Math and Estimation   Page 133

Do your best to use mathematics in your head to solve this problem.
Use the Video Tutorial to check your answer or get help with the problem.

Video Tutorial

Cell["Build Your Skills Pages 134 - 135", "Section"]

Doing Practice Problems

The problems in this section reinforce the math presented in this lesson, and give you opportunities to build on and practice your skills.

•	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!

•	EXTEND YOUR THINKING problems will be more challenging than the others.

Notes

Question 2,    I didn’t do a video for this one.
I could do this, but it’s quite a stretch to think that the tunnel is a “perfect” cylinder.
or half a cylinder....?

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!

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