Volume of Rectangular Prisms — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. A prism is 5×4×6 cm. If the width is doubled, what is the new volume?
A) 120 cm³
B) 240 cm³
C) 480 cm³
D) 360 cm³
The correct answer is B) 240 cm³. A prism is 5×4×6 cm. If the width is doubled, what is the new volume — the answer is 240 cm³.
2. A rectangular box holds exactly 300 cm³. Which set of dimensions could be correct?
A) 10 × 6 × 5 cm
B) 10 × 5 × 5 cm
C) 15 × 5 × 3 cm
D) 12 × 5 × 6 cm
The correct answer is A) 10 × 6 × 5 cm. A rectangular box holds exactly 300 cm³. Which set of dimensions could be correct — the answer is 10 × 6 × 5 cm.
3. A warehouse floor is 20 m × 15 m. Crates stacked 4 m high fill the entire space. What is the total volume?
A) 300 m³
B) 600 m³
C) 1,200 m³
D) 1,500 m³
The correct answer is C) 1,200 m³. A warehouse floor is 20 m × 15 m. Crates stacked 4 m high fill the entire space. What is the total volume — the answer is 1,200 m³.
4. Prism P is 6×8×3 cm and Prism Q is 9×4×3 cm. How do their volumes compare?
A) P is larger by 36 cm³
B) Q is larger by 36 cm³
C) They are equal
D) P is larger by 12 cm³
The correct answer is A) P is larger by 36 cm³. Prism P is 6×8×3 cm and Prism Q is 9×4×3 cm. How do their volumes compare — the answer is P is larger by 36 cm³.
Part B: Fill in the Blank
Write the correct answer on each line.
1. A prism is 4 cm × 5 cm × 3 cm. If every dimension is doubled, the new volume is 480 cm³.
Doubling each dimension gives 8 × 10 × 6 = 480 cm³. When you double all three dimensions, the volume becomes 2 × 2 × 2 = 8 times larger (original was 60 cm³, and 60 × 8 = 480).
2. A freezer is 5 ft × 3 ft × 2 ft. Two identical freezers have a combined volume of 60 ft³.
One freezer holds 5 × 3 × 2 = 30 ft³, so two identical freezers together hold 30 + 30 = 60 ft³.
3. A rectangular garden bed is 10 ft long and 4 ft wide. To hold 120 ft³ of soil, it must be 3 ft deep.
Divide the volume by the length and width: 120 ÷ (10 × 4) = 120 ÷ 40 = 3 ft deep.
4. A cube has a volume of 512 cm³. Each edge is 8 cm long.
Since a cube has equal edges, you need the number that multiplied by itself three times equals 512: 8 × 8 × 8 = 512 cm³.
5. A T-shaped solid has a bottom piece 10×4×2 cm and a top piece 4×4×3 cm. Its total volume is 128 cm³.
Split the T-shape into two prisms: the bottom is 10 × 4 × 2 = 80 cm³ and the top is 4 × 4 × 3 = 48 cm³, so the total is 80 + 48 = 128 cm³.