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 rectangular prism with 4 layers of 15 unit cubes per layer has a volume of 45 cubic units.
Corrected: A rectangular prism with 4 layers of 15 unit cubes per layer has a volume of 60 cubic units.
The corrected sentence is: "A rectangular prism with 4 layers of 15 unit cubes per layer has a volume of 60 cubic units." The error was wrong multiplication — 4 × 15 = 60, not 45: the original sentence "A rectangular prism with 4 layers of 15 unit cubes per layer has a volume of 45 cubic units." needed to be fixed.
2. Fix the sentence:
You can find the volume of a rectangular prism by adding the length, width, and height together.
Corrected: You can find the volume of a rectangular prism by multiplying the length, width, and height together.
The corrected sentence is: "You can find the volume of a rectangular prism by multiplying the length, width, and height together." The error was used addition instead of multiplication: the original sentence "You can find the volume of a rectangular prism by adding the length, width, and height together." needed to be fixed.
3. Fix the sentence:
A prism 9 cm long, 2 cm wide, and 5 cm tall has a volume of 90 cm².
Corrected: A prism 9 cm long, 2 cm wide, and 5 cm tall has a volume of 90 cm³.
The corrected sentence is: "A prism 9 cm long, 2 cm wide, and 5 cm tall has a volume of 90 cm³." The error was wrong units — used square instead of cubic: the original sentence "A prism 9 cm long, 2 cm wide, and 5 cm tall has a volume of 90 cm²." needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. A toy chest is 6 ft × 2 ft × 3 ft. Its volume is 36 ft³.
Multiply 6 × 2 × 3 = 36 ft³. Think of it as 6 rows of 2 cubes, stacked 3 layers high.
2. The three dimensions used in the volume formula are length, width, and height.
The volume formula V = l × w × h requires all three dimensions: length, width, and height, because volume measures 3D space.
3. A prism has a volume of 84 cm³. If the length is 7 cm and the height is 3 cm, the width is 4 cm.
Divide the volume by the two known dimensions: 84 ÷ (7 × 3) = 84 ÷ 21 = 4 cm for the missing width.
4. Each layer of a rectangular prism has 20 cubes and there are 5 layers. The volume is 100 cubic units.
Each layer holds 20 unit cubes, and stacking 5 layers gives 20 × 5 = 100 cubic units total, which is the same as using V = l × w × h.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. A lunch box is 10 in long, 4 in wide, and 5 in tall. A pencil case is 8 in × 3 in × 2 in. Which holds more, and by how much?
Sample answer: The lunch box holds more. It has a volume of 200 in³ and the pencil case has 48 in³, so the lunch box holds 152 in³ more.
A good answer includes: The lunch box holds more. It has a volume of 200 in³ and the pencil case has 48 in³, so the lunch box holds 152 in³ more.
2. A rectangular prism has a volume of 60 cm³. Give one possible set of whole-number dimensions. Show your work.
Sample answer: One set of dimensions is 5 cm × 4 cm × 3 cm because 5 × 4 × 3 = 60 cm³.
A good answer includes: One set of dimensions is 5 cm × 4 cm × 3 cm because 5 × 4 × 3 = 60 cm³.