Math 10-3

Unit 3 Length, Area, and Volume

Lesson 3.3 Surface Area

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/open?id=1EMauePx-P6WrtTIcd7-AtNnmJt8zqXpI

Explore the Math  Page 115

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

Your teacher will let you know which pages you need to do for this lesson.

For an alternate presentation of these ideas,  follow the steps in the next section.

Nets     A website with some examples of 3-D solids that you can turn into nets
https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Geometric-Solids/

Explore the Math (alternate)

This presentation covers the same material as the textbook, but uses a different approach.

Work through the steps that follow to cover the lesson material.

General ideas about surface area vs. volume

Video Tutorial

Nets

The websites below have some examples of 3-d objects that you can then turn into nets.

Nets     A website with some examples of 3-D solids that you can turn into nets
https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Geometric-Solids/

Nets
https://www.geogebra.org/m/pCv2EvwD

Nets

Video Tutorial

The surface area of a cube

Here is a link to a net for a cube
LINK

Print the net, cut it out, and fold it up to form a cube.
You don’t need to do a perfect job, just get the general idea.

Video Tutorial

The surface area of a rectangular prism, aka “box”

Here is a link to a net for a “box”
LINK

Print the net, cut it out, and fold it up to form a box.
You don’t need to do a perfect job, just get the general idea

Video Tutorial

The surface area of a cylinder

Here is a link to a net for a cylinder
LINK

Print the net, cut it out, and fold it up to form a cylinder.
You don’t need to do a perfect job, just get the general idea

Video Tutorial

A detailed presentation that leads to the formula for the surface area of a cylinder.

Video Tutorial 2

The surface area of a cone

Here is a link to a net for a cone
LINK

Print the net, cut it out, and fold it up to form a cone.
You don’t need to do a perfect job, just get the general idea

Video Tutorial

Example 1  Page 118

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 119

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 120

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

Build Your Skills Pages 121 - 122

These questions all come from your textbook.

If you need extra practice or want to maintain your skills,  see the NEXT section for more practice questions.

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 3,    I didn’t do a video for this one.
Even with the solution in the teacher book,  I can’t follow what they have done.
It’s a confusing diagram, and there is no information given about whether we are painting the inside and the outside, etc.

Question 7,    I didn’t do a video for this one.
This would be a good question, but lots of steps, and confusing to know exactly where the carpet is going!
Would you put carpet UNDER the tops of the poles?   Under the base...?  Inside the playhouse?

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 4", "Question 5"}, {"Question 6",  , , , }})

Develop and Maintain Your Skills (extra practice problems)

Doing these problems

These questions are provided to help you develop and maintain your skills with the ideas of this lesson.

These questions are modelled after the questions in the textbook,  so there is nothing different here, just more questions if you need them.

These questions are completely optional (unless your teacher specifically assigns them)

Each question has an answer AND a video solution.

DO your best to answer the question YOURSELF first!

Check your work with the answer provided.

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!

Practice Problems

Problem

A 4-L can of paint covers approximately 38   square meters of wall.

How many cans of paint should be bought to paint the walls of a large room that is 10 m long , 8 m wide and 6 m high 
(with one coat only)?

6

7

9

10

11

Answer

The answer is A

Video Solution Link

Problem

FInd the surface area of the rectangular prism shown below.

Answer

Total surface area  =   14 square meters

Video Solution Link

Problem

Find the surface area of the figure shown below.

Answer

158 square meters

Video Solution Link

Problem

Akiko has been hired to paint the exterior of a storage bin.

If the bin is a rectangular prism that measures 2.3 yards by 4.4 yards by 2.8 yards, what is the surface area of the bin?

Answer

The bin has a surface area of 57.76 (yd^2)

Video Solution Link

Problem

Jim has been hired to make a jewellery box.

If the box is 12 inches long, 6 inches deep, and 9 inches tall, how much veneer will it take to cover the exterior, assuming no waste?

Answer

Jim will need 468 sq in of veneer.

Video Solution Link

Problem

Anita is building a greenhouse onto the side of her garage. 
(a rectangular prism)

She wants it to be 6 feet long, 4 feet wide, and 3 feet high, with the 6-foot long side against the side of her garage.

What area of glass will she need to complete the greenhouse? 
(Hint: No glass will be used along the side of the garage or for the floor.)

Answer

Anita will need 66 sq ft of glass.

Video Solution Link

Problem

Vicki is tiling her (35^(")) by (35^(")) shower stall.

The tiles reach the 8-foot ceiling on 3 sides.

How many square inches of tiles should she purchase to tile the walls and floor?

Answer

Vicki will need 11 305 sq in of tiles.

Video Solution Link

Problem

A canning factory wants to use as little metal as possible to make its cans.

It considers two can sizes that each hold about the same amount.

One is 4.5 inches tall with a radius of 4.2 inches and another is 9.6 inches tall with a radius of 2.8 inches.

Which can should they use? Why?

Answer

Considering surface area, they should use the second can because it uses less material.
Can 1 needs ≈ 229.5 (in^2)  of material
Can 2 needs ≈ 190.07 (in^2)  of material

Video Solution Link

Problem

A cylindrical shipping tube is 48 inches tall and 6 inches in diameter.

a) 	What is its surface area in square inches?

b) 	What is its surface area in square feet?

Answer

a)	The surface area is 961 sq in.
b)	The surface area is about 6.7 square feet.

Video Solution Link

Problem

Sanjiv designs a cylindrical box to hold 4 tennis balls stacked one on top of the other.

If a tennis ball is approximately 3 (1/4) inches in diameter, what is the surface area of the box? 
(Ignore the thickness of the material.)

Answer

The total surface area is approximately 149.2 square inches.

Video Solution Link

Problem

Harry has to paint the walls and ceiling of a room that is 12 feet long, 10 feet wide, and 8 (1/2) feet high.

There is a 6 ft by 4 ft window, a 2 (1/2) ft by 7 ft doorway, and a mirrored closet door that is 6 ft by 7 ft.

What surface area must he paint?

Answer

The total area to be painted is 410.5   (ft^2)

Video Solution Link

Problem

Geneviève plans to apply two coats of paint to the walls of her garden shed.

The shed is 8 feet long by 6 feet wide by 7 feet tall.

If there are 3 windows that are 2 feet by 18 inches each, what will be the total area she paints?

Answer

The total area to be painted is 374 square feet.

Video Solution Link

Problem

A metal cylindrical canister is 1' (3^(")) long and has a diameter of 4 inches.

What is the total surface area of the cylinder?  (in square inches)

Answer

The total surface area is 214 square inches.

Video Solution Link

Problem

Jerg is finishing the sides and bottom of a (rectangular)  hot tub.

The hot tub is 6' (11^(")) long, 5' (6^(")) wide, and 3' deep.

It has a bench going all the way around the inside that is (16^(")) high and (15^(")) wide that will not be finished.

How much finishing material will Jerg need?  (work in feet)

Answer

The total surface area is 113 sq ft. 
Jerg will need 112.7 sq ft of finishing material.

Video Solution Link

Problem

The wood that Terrance wants to use to make a shelving unit costs $6.49/(ft^2) .

How much will it cost him (assuming no wastage) to make a shelving unit that is 4 ft wide by 12 inches deep by 5 ft tall if there are 4 shelves (plus the top and bottom)?

Answer

A diagram will help with the solution.

The total cost of the wood will be $350.46.

Video Solution Link

Problem

Randi is installing flooring in her den.

The room is 12 feet by 19 feet.

A fireplace that is 6 feet wide juts out 2 feet into the room.

Also, there are 2 built-in bookcases, each 1 foot deep and 3 feet wide.

She needs to order 12% more flooring than required because of wastage and cutting.

How much will it cost if the wood costs $5.25/ft ?

Answer

The flooring will cost $1234.80.

Video Solution Link

Problem

Sheet metal costs $54.25/(yd^2) .

How much will it cost Hamish to cover a conical roof if it has a radius of 2.2 yards and a slant height of 3.5 yards?

Answer

The cost of the sheet metal will be $1312.85.

Video Solution Link