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:
If a prism has volume 60 cm³, width 3 cm, and height 4 cm, the length is 60 × 3 × 4 = 720 cm.
Corrected: If a prism has volume 60 cm³, width 3 cm, and height 4 cm, the length is 60 ÷ 3 ÷ 4 = 5 cm.
The corrected sentence is: "If a prism has volume 60 cm³, width 3 cm, and height 4 cm, the length is 60 ÷ 3 ÷ 4 = 5 cm.". The original sentence "If a prism has volume 60 cm³, width 3 cm, and height 4 cm, the length is 60 × 3 × 4 = 720 cm." contained an error that needed to be fixed.
2. Fix the sentence:
A box with volume 36 in³, length 6 in, and width 3 in has height = 36 ÷ 6 = 6 in.
Corrected: A box with volume 36 in³, length 6 in, and width 3 in has height = 36 ÷ 6 ÷ 3 = 2 in.
The corrected sentence is: "A box with volume 36 in³, length 6 in, and width 3 in has height = 36 ÷ 6 ÷ 3 = 2 in.". The original sentence "A box with volume 36 in³, length 6 in, and width 3 in has height = 36 ÷ 6 = 6 in." contained an error that needed to be fixed.
3. Fix the sentence:
To find a missing width, add the volume, length, and height together.
Corrected: To find a missing width, divide the volume by both the length and the height.
The corrected sentence is: "To find a missing width, divide the volume by both the length and the height.". The original sentence "To find a missing width, add the volume, length, and height together." contained an error that needed to be fixed.
Part B: Fill in the Blank
Write the missing word or number on each line.
1. A prism has volume 80 cm³, length 8 cm, and height 2 cm. The width is 5 cm.
V = l × w × h → w = V ÷ l ÷ h = 80 ÷ 8 ÷ 2 = 5 cm.
2. If V = l × w × h, then h = V ÷ l ÷ w.
Solving V = l × w × h for h: divide both sides by l and w to get h = V ÷ l ÷ w.
3. A box has volume 120 in³, width 5 in, and height 4 in. The length is 6 in.
l = V ÷ w ÷ h = 120 ÷ 5 ÷ 4 = 6 in.
4. A rectangular prism has volume 90 m³ and base area 15 m². Its height is 6 m.
V = base area × height → h = V ÷ base area = 90 ÷ 15 = 6 m.
Part C: Short Answer
Answer each question in one or two complete sentences.
1. A fish tank has volume 72 cubic inches, length 6 inches, and height 3 inches. What is the width?
Sample answer: The width is 72 ÷ 6 ÷ 3 = 4 inches.
Use the formula w = V ÷ l ÷ h = 72 ÷ 6 ÷ 3 = 4 inches.
2. Explain how finding a missing dimension is the opposite of finding volume.
Sample answer: Finding volume multiplies all three dimensions, so finding a missing dimension divides to undo that multiplication.
V = l × w × h uses multiplication; finding a missing side reverses it with division.