Activities

1. What does the “B” in the volume formula for a rectangular prism, V = Bh, represent?
   
   
2. What dimension is represented by the “b” in the picture below?

3. Use the diagram to answer the question.  What is the height of the rectangular prism?

4. What is the volume of a rectangular prism with a base area of 12 in² and a height of 3 inches?

5. What is the volume of a rectangular prism with a height of 2 feet, length of 4 feet, and a width of 3 feet?

6. What is the volume of the rectangular prism in cubic centimeters?        

7. Allison is charged with filling the swimming pools at the outdoor park.  The pools are rectangular prisms with a length of 10 m, a width of 3 m, and a height of 1 m.  The pool is to be filled half full with water.  How many cubic meters of water must she put into the pool?

8. Find the volume of the following figure if the area of the base is 10 cm². 

9. What is the height of a rectangular prism with a volume of 240 ft³, and the area of the base equal to 40 ft²?

10. What is the width of a rectangular prism with a volume of 84 cm³, height of 2 cm and width of 6 cm?
    
    
11. The dimensions of a rectangular prism are 4 cm x 3 cm x 10 cm.  How many buckets of water will it take to fill the prism if each bucket holds 6 cubic centimeters of water?

12. Alex is the gardener for the Rameski family.  A new pool was built in the backyard and he must provide Mr. Rameski with an estimate on the cost of filling the pool.  Water is pumped in and the charge is $0.10 per gallon (they will not sell partial gallons).  The pool is a rectangular prism with dimensions l = 22 feet, w = 12 feet and h = 8 feet.  1 cubic foot is equal to approximately 7.48 gallons.  How many gallons will be necessary to fill the pool 12 inches from the top?  What is the cost?  Show all work and explain.

13. Carmen fills the fish tank at the zoo.  The tanks are rectangular prisms with dimensions l = 7 m, w = 3 m, and h = 1 m.  The tank is to be filled 20 cm from the top with water.  How many cubic meters of water must he put into the tank? Show all work and explain.

14. Acme Company has some leftover boxes with base dimensions 2 ft. x 3 ft. and a height of 5 ft. 2 inches.  They want to pack each box with as many 3-inch Rubik cubes as possible.  How many cubes will fit into a packing box?  What is the volume of the packing material that must take up the remaining space in the box?  Explain.

15. Explain where Donna made an error in her calculations of the volume of the rectangular prism.

16. The volume of both the rectangular prisms are equal.   Explain how you determined the missing dimensions.

17. The volume of a rectangular prism is 36 cubic meters.  Identify two possible dimensions and explain why there are many more.

Answer Key/Rubric

1. Area of the base or length times width because the base is a rectangle.
   
   
2. The “b” represents the width of the rectangular prism.
   
   
3. The height of the rectangular prism is represented by the “y”.

4. 36 in³
   
   
5. 24 ft³
   
   
6. 52,800 cm³
   
   
7. 15 m³
   
   
8. 350 cm³
   
   
9. 6 ft.
   
   
10. 7 cm
    
    
11. 20 buckets

12. 13,824 gallons needed; $1,382.40 total cost
    Acceptable explanations may include, but are not limited to:

• Since the water is to be filled 12 inches from the top, the height becomes 7 feet instead of 8 feet.
• Find the volume of the pool, multiply 22 x 12 x 7, which equals 1,848 cubic feet. 
• Multiply 1,848 by 7.48 gallons because there are 7.48 gallons in one cubic foot.  This equals 13,823.04 gallons. 
• You cannot buy partial gallons so round up to 13,824 gallons to make sure you have enough
• Multiply by 13,824 by $0.10, which is the cost per gallon.  13,824 x .10 = $ 1,382.40 which is the total cost.

13. 16.8 cubic meters
    Acceptable explanations may include, but are not limited to:

• He is filling the tank 20 cm from the top so 100 cm (height = 1 m = 100 cm) – 20 cm = 80 cm. 
• Converting 80 cm into meters is dividing by 100, 80/100 = .8
• The dimensions of the tank that will be filled with water are 7m x 3 m x .8 m= 16.8 cubic meters.

14. 1,920 Rubik cubes; 1,728 cubic inches of packing material
    Acceptable explanations may include, but are not limited to:

• Convert the dimensions of the box into inches (student shows or explains these calculations).  24 in x 36 in x 62 in. 
• Divide each number by 3 to see how many cubes will fit in each dimension
• 8 cubes by 12 cubes is the first layer = 96 cubes, which completely fills the first layer of the box. 
• 20 rows of cubes will fit the height with 2 inches left
• 8 x 12 x 20 = 1,920 is the number of cubes that will fit into the box. 
• The volume of the space not filled by Rubik cubes is 2 in x 24 in x 36 in = 1,728 cubic inches.

15. Acceptable explanations may include, but are not limited to:

• Donna mixed two different measurements together in her problem; feet and inches
• She left the 1 ft. in the equations, but used 12 inches as she was supposed to for the multiplication
• Used the wrong label on the answer.  The answer should have been 648 cubic inches not feet. 

16. Acceptable explanations may include, but are not limited to:

• The volume of the cube is 12 x 12 x 12 = 1,728 cubic cm. 
• The volumes are equal so the rectangular prism is also 1,728 cubic cm. 
• The dimensions of the base are ½ that of the cube, the length and width are 6 cm. 
• The volume of the second rectangular prism is 1,728 = 6 x 6 x height simplified to 1,728 = 36 x height.  Dividing both sides of the equation by 36 gives a height of 48 cm.
• Dimensions of the rectangular prism: length = 6cm; width = 6 cm; height = 48 cm

17. Possible answers include, but are not limited to: 9 x 2 x 2; 4 x 3 x 3
    Acceptable explanations may include, but are not limited to:

• Volume of a rectangular prism is V = l x w x h, essentially we need three numbers that when multiplied together give the same solution, which is found by listing the factors of the volume.
• Can construct a tree diagram to find all the factors of the volume
• Factors for 36 are 2 x 2 x 3 x 3; these can then be combined to make different lengths, widths, and heights
• There are many more because I did not use 1 as a factor and also did not use any fractions or decimals as factors.