Volume of Rectangular Prisms — Answer Key
Part A: Multiple Choice
Circle the best answer for each question.
1. An L-shaped figure is made of two prisms: one 3×4×2 cm and one 5×4×2 cm. What is the total volume?
A) 54 cm³
B) 64 cm³
C) 48 cm³
D) 72 cm³
The correct answer is B) 64 cm³. An L-shaped figure is made of two prisms: one 3×4×2 cm and one 5×4×2 cm. What is the total volume — the answer is 64 cm³.
2. A rectangular prism has a volume of 240 cm³ and a base area of 40 cm². What is its height?
A) 4 cm
B) 8 cm
C) 6 cm
D) 10 cm
The correct answer is C) 6 cm. A rectangular prism has a volume of 240 cm³ and a base area of 40 cm². What is its height — the answer is 6 cm.
3. A pool is 10 m × 5 m × 2 m. How many cubic meters of water does it hold?
A) 50 m³
B) 100 m³
C) 200 m³
D) 70 m³
The correct answer is B) 100 m³. A pool is 10 m × 5 m × 2 m. How many cubic meters of water does it hold — the answer is 100 m³.
4. If you triple all three dimensions of a 2×3×4 cm prism, what is the new volume?
A) 72 cm³
B) 216 cm³
C) 648 cm³
D) 324 cm³
The correct answer is C) 648 cm³. If you triple all three dimensions of a 2×3×4 cm prism, what is the new volume — the answer is 648 cm³.
Part B: Fill in the Blank
Write the correct answer on each line.
1. A step-shaped solid is made of a bottom prism 8×6×3 cm and a top prism 4×6×2 cm. The total volume is 192 cm³.
Add the two prism volumes: the bottom is 8 × 6 × 3 = 144 cm³ and the top is 4 × 6 × 2 = 48 cm³, giving 144 + 48 = 192 cm³.
2. A planter box is 2 ft × 1 ft × 3 ft. Four identical planters hold 24 ft³ of soil in total.
One planter holds 2 × 1 × 3 = 6 ft³, so four identical planters hold 6 × 4 = 24 ft³ of soil altogether.
3. A prism has a volume of 180 cm³. If the length is 9 cm and the width is 4 cm, the height is 5 cm.
Use the volume formula in reverse: 180 ÷ (9 × 4) = 180 ÷ 36 = 5 cm for the height.
4. Two prisms share the same volume. One is 6×5×h cm and the other is 10×3×4 cm. The value of h is 4.
The second prism's volume is 10 × 3 × 4 = 120 cm³, and since the first prism has the same volume, solve 6 × 5 × h = 120, so h = 120 ÷ 30 = 4.
5. A shipping container is 12 m × 2 m × 3 m. Its volume is 72 m³.
Multiply 12 × 2 × 3 = 72 m³, which tells you how many cubic-meter blocks would fill the container.