Math 10-3

Unit 3 Length, Area, and Volume

Lesson 3.4 Volume

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 Pages 124 - 125

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.

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.

Step 1   Introduction to Volume

Introduction to Volume 		Video Tutorial

An animation that illustrates the concept of volume  	Video Tutorial

Step 2 Investigate volume A

Adjust the sliders to control the size and shape of the rectangular prism.

The length, width, and height can vary from 0 to 5 units

You can also control the opacity (transparency),  going from a wireframe model where all you see are edges, to a solid model where you can't see through the faces at all.

An opacity of 0  is completely transparent,  an opacity of 1 is complete "un-transparent"

The volume of an object is how much space it takes up.

Step 3 Investigate volume B

Adjust the sliders to control the size and shape of the rectangular prism.

The length, width, and height can vary from 0 to 5 units

The volume of an object is how much space it takes up.

You can think of measuring volume by counting the number of unit cubes  it takes to fill an object

In this demonstration you can go from a volume of ZERO to a volume of 125 cubic units (125 single cubes)

Step 4 Investigate volume C

Adjust the sliders to control the size and shape of the rectangular prism.

The length, width, and height can vary from 0 to 5 units

The volume of an object is how much space it takes up.

You can think of measuring volume by counting the number of unit cubes  it takes to fill an object

In this demonstration you can go from a volume of ZERO to a volume of 125 cubic units (125 single cubes)

The volume of a rectangular prism is the area of the base times the height

Step 5   A universal volume formula for regular solids

Video Tutorial

Step 6 Volume conversions

Video Tutorial

Step 7  Capacity  (Definition)

A website with an animation that illustrates the idea of capacity
LINK

Step 8 Converting Units

Video Tutorial

Example 1  Page 127

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 128

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  Pages 128 - 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.

NOTE!    The textbook didn’t really word this question correctly.
If you want to try this yourself,  calculate the COST of filling the planters with soil from both stores,  then compare.

Video Tutorial

Build Your Skills Page 132

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.

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", , , }})

Develop and Maintain Your Skills

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

The area of the base of a fish tank is 1090 (cm^(2 ))

The height of the tank is 30 cm

Find the volume of the fish tank

Answer

The volume of the fish tank is 32 700 cubic centimeters

Video Solution Link

Problem

A deck of 54 cards  (52 regular cards and 2 jokers)  fits in a box shaped like a right rectangular prism.

The box has dimensions  6.3 cm  ×  9.0 cm  by  1.5  cm

What is the volume of the box?

Give the answer to the nearest cubic centimeter

Answer

To the nearest cubic centimeter, the volume of the box is  85 (cm^3)

Video Solution Link

Problem

Alfred has a bulk container that holds 2000 cubic inches of dog biscuits.

He plans to sell the biscuits in small boxes that measure (5^(")) by 8" by 6".

How many boxes will he need to sell all the dog biscuits?

Answer

Alfred will need 9 boxes to sell all the biscuits

Video Solution Link

Problem

A fish tank is a rectangular prism that is 30 inches long, 24 inches deep, and 18 inches high.

How much water will it hold:

a) 	in cubic inches?
b) 	in cubic feet?

Answer

a)	12960 (in^3)
b)	7.5 (ft^3)

Video Solution Link

Problem

Will the contents of a box that is 3 inches by 4 inches by 6 inches fit into a cube with sides of 4 inches?

Answer

No, the contents won’t fit.

Video Solution Link

Problem

Paulino runs a landscaping business.

He needs to cover an area that is 10.8 m by 9.5 m with 10 cm of topsoil.

How much will it cost if the soil costs $18.75/(yd^3), and soil is available in multiples of  (1/2) (yd^3) ?

Answer

It will cost $253.13 to buy the soil

Video Solution Link

Problem

A garden bed is 4' by 3', and a 6 inch layer of soil will be spread over the garden.

A bag of soil contains 2 (ft^3) of soil.

How many bags are needed to cover the garden?

Answer

3 bags are needed to cover the garden.

Video Solution Link

Problem

Serina is travelling through the US and her car’s gas tank has a capacity of 55 litres.

a) 	How much is this in American gallons?

b) 	If gas costs $2.99/gal in Bellingham, WA, how much will it cost to fill her car (assuming that it is totally empty)?

c) 	Assuming she has the same car in London, England, where gas costs $9.86/gal (converted from pounds), how much will it cost to fill her tank? 
	(Remember that the British gallon is a different size.)

Answer

a)	15 gallons (rounded)
b)	$44.85
c)	$118.32

Video Solution Link

Problem

A recipe calls for 2 (3/4) cups of milk. How much is this in mL?

Answer

687.5 mL

Video Solution Link

Problem

If your car’s fuel consumption rate is 8.8 L/100 km, how many US gallons will you need for a trip of approximately 450 km?

Answer

10.5 US gallons will be needed

Video Solution Link

Problem

The exterior of a concrete container will be 10 feet by 8 feet by 4 feet tall.

The walls and the bottom are 6 inches thick.

What will it cost to construct it if concrete is $98.95/cubic yard?

Answer

$364.65

Video Solution Link