Volume of Rectangular Prisms — Answer Key
Part A: Fix the Sentence
Each sentence has an error. Rewrite it correctly on the line.
1. Fix the sentence:
A fish tank 10 in long, 5 in wide, and 8 in tall holds 400 in² of water.
Corrected: A fish tank 10 in long, 5 in wide, and 8 in tall holds 400 in³ of water.
The corrected sentence is: "A fish tank 10 in long, 5 in wide, and 8 in tall holds 400 in³ of water." The error was wrong units — used square instead of cubic: the original sentence "A fish tank 10 in long, 5 in wide, and 8 in tall holds 400 in² of water." needed to be fixed.
2. Fix the sentence:
A rectangular prism 7 cm × 3 cm × 2 cm has a volume of 42 cm³ because 7 + 3 + 2 = 42.
Corrected: A rectangular prism 7 cm × 3 cm × 2 cm has a volume of 42 cm³ because 7 × 3 × 2 = 42.
The corrected sentence is: "A rectangular prism 7 cm × 3 cm × 2 cm has a volume of 42 cm³ because 7 × 3 × 2 = 42." The error was described addition instead of multiplication: the original sentence "A rectangular prism 7 cm × 3 cm × 2 cm has a volume of 42 cm³ because 7 + 3 + 2 = 42." needed to be fixed.
3. Fix the sentence:
A shoebox that is 12 in × 6 in × 4 in has the same volume as a box that is 12 in × 3 in × 4 in.
Corrected: A shoebox that is 12 in × 6 in × 4 in has a greater volume than a box that is 12 in × 3 in × 4 in.
The corrected sentence is: "A shoebox that is 12 in × 6 in × 4 in has a greater volume than a box that is 12 in × 3 in × 4 in." The error was volumes are different — 288 in³ vs 144 in³: the original sentence "A shoebox that is 12 in × 6 in × 4 in has the same volume as a box that is 12 in × 3 in × 4 in." needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. A cereal box that is 8 in × 3 in × 12 in has a volume of 288 in³.
Multiply 8 × 3 × 12 to get 288 in³, because volume is always found by multiplying length times width times height.
2. Volume is always measured in cubic units because it fills three-dimensional space.
Volume measures how much space a 3D shape takes up, so it uses cubic units (like cm³ or in³) because you are multiplying three dimensions together.
3. A rectangular prism has a volume of 120 cm³. If the length is 10 cm and the width is 4 cm, the height is 3 cm.
Since V = l × w × h, you can find the missing height by dividing: 120 ÷ (10 × 4) = 120 ÷ 40 = 3 cm.
4. A gift box is 5 in × 5 in × 5 in. Its volume is 125 in³.
When all three dimensions are 5 inches, the box is a cube and its volume is 5 × 5 × 5 = 125 in³.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. A storage bin is 4 ft long, 2 ft wide, and 3 ft tall. Will 30 unit cubes that are each 1 ft³ fit inside? Explain.
Sample answer: No, because the bin's volume is 4 × 2 × 3 = 24 ft³, which is less than 30 ft³.
A good answer includes: No, because the bin's volume is 4 × 2 × 3 = 24 ft³, which is less than 30 ft³.
2. Explain in your own words what happens to the volume of a rectangular prism when you double one of its dimensions.
Sample answer: The volume doubles because volume is the product of all three dimensions, and doubling one factor doubles the entire product.
A good answer includes: The volume doubles because volume is the product of all three dimensions, and doubling one factor doubles the entire product.