Activities

1. Identify the dimensions of the base of the red rectangular prism.

2. True or false.  The volume of two rectangular prisms that are connected but not overlapping can be calculated by finding the volume of one and doubling it.
   
   
3. True or false.  The volume of two connected non-overlapping rectangular prisms can be calculated by calculating the volume of each prism then adding them together.

4. What is the volume of two identical connected rectangular prisms with a base area of 24 cm² and a height of 2 cm?

5. The dimensions of the white rectangular prism are half the dimensions of the grey rectangular prism. What is the total volume?    

6. The shape below is comprised of two rectangular prisms.  What is the volume in cubic centimeters?     

7. The figure below is two non-overlapping rectangular prisms. They have identical bases and different heights.   Which expression can be used to find the total volume?

8. The figure below is two non-overlapping rectangular prisms with identical bases.  Which expression cannot be used to find the total volume?

9. Sara is asked to find the volume of two connected rectangular prisms.  Explain why it is very important for Sara to know if the prisms are overlapping or non-overlapping prisms.

10. Explain how to calculate the total volume of the figure below.  Be sure to include the answer in your explanation.

11. Doug and Kirk are asked to find the volume of the connected, but not overlapping, set of two rectangular prisms. Who is correct?  Identify the mistake made by the person who got it wrong.

Rectangular Prism 1: l = 12 in; w = 3 in; h = 7 in
Rectangular Prism 2: B = 24 in²; w = 2 ft.

Doug    12 x 3 x 7  = 252                      Kirk      12 x 3 x 7 = 252 in³
            24 x 2 = 48                                          24 x 24 = 576 in³
            48 + 252 = 300 in²                               252 + 576 = 828 in³

12. There are nine 15 cm metal cubes and ten 25 cm metal cubes that are melted and poured into a 1 m iron cube.  Will all the liquid metal fit in the box?  If so, how much extra room is in the iron box?  If not, how much metal overflows the iron box? Explain.

13. The diagram below shows two non-overlapping rectangular prisms with the same height.
    The volume of Prism #1 is 324 in³.  Find the dimensions of Prism #1 and the total volume of the entire shape. Show all your work.  Explain how you found the dimensions for Prism #1.       

9. Sara is asked to find the volume of two connected rectangular prisms.  Explain why it is very important for Sara to know if the prisms are overlapping or non-overlapping prisms.

10. Explain how to calculate the total volume of the figure below.  Be sure to include the answer in your explanation.

11. Doug and Kirk are asked to find the volume of the connected, but not overlapping, set of two rectangular prisms. Who is correct?  Identify the mistake made by the person who got it wrong.

Rectangular Prism 1: l = 12 in; w = 3 in; h = 7 in
Rectangular Prism 2: B = 24 in²; w = 2 ft.

Doug    12 x 3 x 7  = 252                      Kirk      12 x 3 x 7 = 252 in³
            24 x 2 = 48                                          24 x 24 = 576 in³
            48 + 252 = 300 in²                               252 + 576 = 828 in³

12. There are nine 15 cm metal cubes and ten 25 cm metal cubes that are melted and poured into a 1 m iron cube.  Will all the liquid metal fit in the box?  If so, how much extra room is in the iron box?  If not, how much metal overflows the iron box? Explain.

13. The diagram below shows two non-overlapping rectangular prisms with the same height.
    The volume of Prism #1 is 324 in³.  Find the dimensions of Prism #1 and the total volume of the entire shape. Show all your work.  Explain how you found the dimensions for Prism #1.       

Answer Key/Rubric

1. 3 x 4
   
   
2. False
   
   
3. True

4. 96 cm³
   
   
5. A
   
   
6. 5,376 cm³
   
   
7. B
   
   
8. C

9. Acceptable responses may include, but are not limited to:

• If the figures are overlapping then the volume of the overlap is being counted twice. 
• The volume of the each prism is calculated and then added together, therefore the overlap would be figured in each prism instead of only once

10. Acceptable responses may include, but are not limited to:

• Volume = length x width x height
• The bottom prism has different measurements; change 1m into cm; 1 m = 100 cm
• The volume of the prism on the bottom is V = 8 x 6 x 100 which is 4,800 cubic centimeters.
• The volume of the prism on top is V = 12 x 8 x 6 (the 6 is the same width as the bottom prism) which is 576 cubic centimeters.  
• Add the two prisms together:  4,800 + 576 = 5,376 cubic centimeters.

11. Kirk is correct.
    Doug’s mistake was he forgot to convert 2 ft. into 24 inches.  Cannot use two different units of measure.

12. The iron box will not overflow; 813,375 cubic centimeters of extra room
    Acceptable explanations may include, but are not limited to:

• Volume of first set of cubes:  9 x 15 x 15 x 15 = 30,375 cm³
• Volume of second set of cubes:  10 x 25 x 25 x 25 = 156,250 cm³
• Total volume of melted metal cubes:  30,375 + 156,250 = 186,625 cm³
• Iron box measurement given in meters, must be converted to centimeters
• 1 m = 100 cm
• Volume of iron box:  100 x 100 x 100 = 1,000,000 cm³
• Since 186,625 cm³ is smaller than 1,000,000 cm³, the liquid metal will fit into the iron box
• Extra room:  1,000,000 - 186,625 = 813,375

13. Dimensions of prism #1: h = 18 in; l = 2 in; w = 9 in
    Total volume is 540 in³
    Acceptable explanations may include, but are not limited to:

• Length of 2 inches was given in the diagram
• Height of 18 inches is from prism #2; told they are the same in the problem
• Width of 9 inches:
  • Set up volume formula with known information:  324 = 2 x w x 18
  • Simplify:  324 = 36w
  • Divide both sides by 36 to get: w = 9