Math






Unit 2 - Volume  [ Review / Study Guide ] - ANSWER KEY
Name______________________________                                     # ____________
Tell if the following statements are true or false by calculating and then writing true or false in the box beside the equation.
  1. 4 x 6 = 6 + (2 x 9)         True
             24   =    24
    2.    50 - 10 = 5 x 8         
                40    =    40                 True
    3.   30    2 = 5 x 3
               15    =    15                   True
    4.     25 + 4  = 3 x 9
                29    =   27                   False
5.  Explain in your own words what it means to find the volume of a 3-dimensional figure?
When finding the volume, you are finding the amount of space inside a solid figure OR the amount of space the solid figure takes up.
6.  Wesley said that you can calculate the volume of a rectangular prism by finding the area of the base and multiplying that by the number of layers there are.  Is this correct?  Why or why not?  Explain and justify your answer.  You MAY use words, equations or pictures to explain.
Yes, Wesley is correct.  One way of finding volume is: Length x Width x Height.  When you multiply Length x Width, that’s the same as finding the AREA OF THE BASE.  The Height is the same thing as the number of layers there are, so Wesley is correct.
7.  The figure below is made of cubes.  Each cube measures 1 centimeter by 1 centimeter by 1 centimeter.  What is the volume of the figure below?


5 cm x 2 cm x 3 cm = 30 cubic cm.
Volume = ____30________ cubic cm.
8.  The bottom layer in a rectangular prism has an area of 8 square units.  The prism has a height of 4 units.  What is the total volume of the prism?
V = base x height
8 x 4 = 32  →  The total volume of the prism is 32 cubic units.
9.  Jackson received a toy box for his birthday.  The volume of the box is 180 cm3.  The box measured 10 cm high.
  1. What is the area of the base?
                       18
     b.  List ALL the possible dimensions of the base.
                      1 x 18  ,       2 x 9 ,      3 x 6


10.  A rectangular prism is shown below.  What is the volume of the rectangular prism?  Show your work.
                                                                                            
               4 x 2 x 3 = 24 → The volume is 24 cubic feet.
11.    Each cube represents 1 cubic unit.  The box below has 8 cubic units inside so far.  How many cubic units fit in the box when it is full?
              4 x 4 x 2 = 32
               When the box is full, 32 cubic units will fit inside.
12. What is the volume of the figure below?  Show your work.
 
                                                            The volume is 140 cubic feet.
                                                      (Your answer should also include equations or pictures.)
13.  Find the volume of the figure.   
Explain your answer in words, equations or pictures.


The volume is 96 cubic meters.
(Your answer should also include equations or pictures.)
14.  Bella and Daniel want to increase the volume of this prism by 60 cubic centimeters.  Bella wants to add four layers and Daniel says they need to add 10 layers.  Their teacher tells them they are both correct.  Explain how this is possible.  [You must explain using WORDS]  You may also draw a picture to help you.
                                                                                                     
                                          

                                                        
                                               
                         
Conclusion:
Bella wanted to add 4 layers of 15 which is 60 cubes total.  Daniel wanted to add 10 layers of 6 which is also 60 cubes total.  They are both correct because both ways add up to 60 cubes.
15.  A rectangular tank with a base area of 32 cm2 is filled with water and oil to a depth (height) of 12 cm.  The oil and water separate into two layers when the oil rises to the top.  If the thickness of the oil layer is 5 cm, what is the volume of the water?  [HINT: 1st, figure out what the thickness (depth) of the water is.]
                                  
                                                                        V = base x height
         32 x 7 = 224 cubic cm.

The volume of just the water is 224 cubic cm.
Name______________________________                                     # ____________
Tell if the following statements are true or false by calculating and then writing 
true or false in the box beside the equation.
  1. 4 x 6 = 6 + (2 x 9)       
          
    2.    50 - 10 = 5 x 8         
                           
    3.   30    2 = 5 x 3
                          
    4.     25 + 4  = 3 x 9
                
5.  Explain in your own words what it means to find the volume of a 3-dimensional figure?
6.  Wesley said that you can calculate the volume of a rectangular prism by finding the area of the base and multiplying that by the number of layers there are.  Is this correct?  Why or why not?  Explain and justify your answer.  You MAY use words, equations or pictures to explain.

7.  The figure below is made of cubes.  Each cube measures 1 centimeter by 1 centimeter by 1 centimeter.  What is the volume of the figure below?

Volume = ____________ cubic cm.

8.  The bottom layer in a rectangular prism has an area of 8 square units.  The prism has a height of 4 units.  What is the total volume of the prism?
9.  Jackson received a toy box for his birthday.  The volume of the box is 180 cm3.  The box measured 10 cm high.
  1. What is the area of the base?
                       
     b.  List ALL the possible dimensions of the base.
                     
10.  A rectangular prism is shown below.  What is the volume of the rectangular prism?  Show your work.
                                                                                            
             
11.    Each cube represents 1 cubic unit.  The box below has 8 cubic units inside so far.  How many cubic units fit in the box when it is full?
             

12. What is the volume of the figure below?  Show your work.
 
                                                        

13.  Find the volume of the figure.   
Explain your answer in words, equations or pictures.

14.  Bella and Daniel want to increase the volume of this prism by 60 cubic centimeters.  Bella wants to add four layers and Daniel says they need to add 10 layers.  Their teacher tells them they are both correct.  Explain how this is possible.  [You must explain using WORDS]  You may also draw a picture to help you.
                                                                                                     
                                          
                                                        
                               
15.  A rectangular tank with a base area of 32 cm2 is filled with water and oil to a depth (height) of 12 cm.  The oil and water separate into two layers when the oil rises to the top.  If the thickness of the oil layer is 5 cm, what is the volume of the water?  [HINT: 1st, figure out what the thickness (depth) of the water is.]
                                  
                                                                       


Volume:






Multiplication:








Order of Operations:







Study Guide for Unit 1 Test - Place Value and Whole Number Operations
DUE Wednesday- TEST-FRIDAY, October 9th

Name___________________________ Date___________________
Place Value:
1.  In the number 466, 721; explain the difference between the two 6s.





2.    2,356,819
What is the value of the 8?   

_______________________
What place value is the 5 in?

_______________________
3.  Write a number that is 10 times smaller than 4,000.


4.  Write a number that is 10 times bigger than 30.
Order of Operations:
5.
    27 (2 + 7) = ___________




6.  
    5 x 3 + 3 x 4 = ____________
7.  
    20 + [(17 - 5) 3] = ________



8.  
    30 5 x 7 + 11 = __________
Multiplication and Division: Read each problem carefully and solve using the most efficient and accurate strategy for you.
9.  
            25 x 34 = ____________








10.  
              1,130 3 = _____________
11.  A college football stadium has 34 sections of seats.  Each section contains 352 seats.  What is the seating capacity of the stadium?











12.  The 5th grade earned $142 from a bake sale.  They decide to donate an equal amount of money to four different organizations. How much money will the class donate to each organization?





13.  A class of 242 students is going on a field trip.  The buses used to transport the students hold 28 students.  How many buses will be needed to take all the students on the field trip?  Show your work.







14.  
          251 x 78 = ______________
15.  Mary is cutting a piece of paper to make a poster.  The length of the paper is 32 inches and the width of the paper is 14 inches.  How many square inches in area is the paper?
(Area= L X W)



16.  Tom wants a garden that has an area of 884 square feet.  He knows the dimension of one side of the garden is 26 feet.  What is the length of the other side of the garden?

                   26 ft







17.  
              3,472 14 = ______________



18.  
     Elephants can eat up to 345 pounds of vegetation and drink up to 40 gallons of water each day.  How much vegetation could an elephant eat in a year? (Hint:  1 year = 365 days)







19.  There are 2,055 students in a national research project.  The project leaders formed teams of 15 students.  How many teams did they form?






20.  There are 14 players on each soccer team in the Smithville Soccer League.  How many players are in the league if there are 24 teams?
Take the following multiplication quiz and print when you are finished.  MAKE SURE YOUR NAME is on your quiz!

http://www.multiplication.com/learn/quiz/9/x/9/fact
Multiplication Quiz
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