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:
The volume of a box 4 cm long, 3 cm wide, and 2 cm tall is 24 cm².
Corrected: The volume of a box 4 cm long, 3 cm wide, and 2 cm tall is 24 cm³.
The corrected sentence is: "The volume of a box 4 cm long, 3 cm wide, and 2 cm tall is 24 cm³.". The original sentence "The volume of a box 4 cm long, 3 cm wide, and 2 cm tall is 24 cm²." contained an error that needed to be fixed.
2. Fix the sentence:
To find the volume of a rectangular prism, multiply length times width.
Corrected: To find the volume of a rectangular prism, multiply length times width times height.
The corrected sentence is: "To find the volume of a rectangular prism, multiply length times width times height.". The original sentence "To find the volume of a rectangular prism, multiply length times width." contained an error that needed to be fixed.
3. Fix the sentence:
A prism 5 in long, 2 in wide, and 3 in tall has a volume of 13 in³.
Corrected: A prism 5 in long, 2 in wide, and 3 in tall has a volume of 30 in³.
The corrected sentence is: "A prism 5 in long, 2 in wide, and 3 in tall has a volume of 30 in³.". The original sentence "A prism 5 in long, 2 in wide, and 3 in tall has a volume of 13 in³." contained an error that needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. Volume measures the amount of space inside a three-dimensional shape.
Volume is the amount of three-dimensional space enclosed within a solid figure.
2. A rectangular prism with length 6 cm, width 4 cm, and height 2 cm has a volume of 48 cm³.
V = l × w × h = 6 × 4 × 2 = 48 cm³.
3. A unit cube has a volume of 1 cubic unit.
A unit cube has sides of length 1, so its volume = 1 × 1 × 1 = 1 cubic unit.
4. A box that is 3 m long, 3 m wide, and 3 m tall has a volume of 27 m³.
V = 3 × 3 × 3 = 27 m³. This is also 3³ = 27.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. A rectangular prism has 5 layers of unit cubes with 12 cubes per layer. What is the total volume?
Sample answer: The total volume is 60 cubic units because 12 × 5 = 60.
Each layer is a base of 12 unit cubes. 5 layers × 12 cubes = 60 cubic units total.
2. Why do we measure volume in cubic units instead of square units?
Sample answer: Volume measures three-dimensional space, so cubic units account for length, width, and height.
Area uses square units for 2D (length × width). Volume adds a third dimension, so units become cubic.