Volume starts with knowing what cubic units actually mean. You'll fix sentences that mix up cm² and cm³, swap addition for multiplication on a 7×3×2 cm prism, and compare a 12×6×4 in shoebox with a 12×3×4 in box that turns out to hold half as much.
Fill-in problems lock in V = l × w × h on a cereal box (8×3×12 in) and a 5×5×5 in gift box, then flip the formula to find the missing height when volume is 120 cm³. Short-answer problems push you to reason: will 30 unit cubes fit a 4×2×3 ft bin, and what happens to volume when you double one dimension? You leave able to spot unit errors and explain three-dimensional space.
Style:
Volume of Rectangular Prisms
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.
Rewrite: A fish tank 10 in long, 5 in wide, and 8 in tall holds 400 in³ of water.
2. Fix the sentence:
A rectangular prism 7 cm × 3 cm × 2 cm has a volume of 42 cm³ because 7 + 3 + 2 = 42.
Rewrite: A rectangular prism 7 cm × 3 cm × 2 cm has a volume of 42 cm³ because 7 × 3 × 2 = 42.
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.
Rewrite: 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.
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.
2. Volume is always measured in cubic units because it fills three-dimensional space.
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.
4. A gift box is 5 in × 5 in × 5 in. Its volume is 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.
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.
The volume doubles because volume is the product of all three dimensions, and doubling one factor doubles the entire product.
Volume of Rectangular Prisms
★ 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.
Rewrite: A fish tank 10 in long, 5 in wide, and 8 in tall holds 400 in³ of water.
2) Fix the sentence:
A rectangular prism 7 cm × 3 cm × 2 cm has a volume of 42 cm³ because 7 + 3 + 2 = 42.
Rewrite: A rectangular prism 7 cm × 3 cm × 2 cm has a volume of 42 cm³ because 7 × 3 × 2 = 42.
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.
Rewrite: 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.
★ 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.
2) Volume is always measured in cubic units because it fills three-dimensional space.
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.
4) A gift box is 5 in × 5 in × 5 in. Its volume is 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.
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.
The volume doubles because volume is the product of all three dimensions, and doubling one factor doubles the entire product.
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