Volume of Rectangular Prisms — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. A fish tank is 12 in × 6 in × 8 in. It can hold 576 in³ of water.
Multiply 12 × 6 × 8 = 576 in³. This tells you how many 1-inch cubes of water would fit inside the tank.
2. A moving box is 3 ft × 2 ft × 4 ft. Its volume is 24 ft³.
Multiply 3 × 2 × 4 = 24 ft³. Each foot-cube is a 1 ft × 1 ft × 1 ft block, and 24 of them would fill this box.
3. When you halve the height of a prism, you halve its volume.
Because volume is a product of three dimensions, cutting one dimension in half cuts the entire volume in half, since you are multiplying by half the original value.
4. A sandbox is 8 ft long, 6 ft wide, and 1 ft deep. It needs 48 ft³ of sand to fill completely.
Multiply 8 × 6 × 1 = 48 ft³. Even though the sandbox is only 1 foot deep, it still covers a large area so it needs 48 cubic feet of sand.
5. A cube with edge length 7 cm has a volume of 343 cm³.
A cube has all edges the same length, so volume = 7 × 7 × 7 = 343 cm³.
6. A suitcase is 24 in × 16 in × 10 in. Its volume is 3840 in³.
Multiply step by step: 24 × 16 = 384, then 384 × 10 = 3,840 in³.
7. V = B × h means volume equals the area of the base times the height.
In the formula V = B × h, the letter B stands for the area of the base (length × width), so you multiply that flat area by the height to get the full 3D volume.
8. A prism has a volume of 180 cm³, a length of 9 cm, and a height of 5 cm. Its width is 4 cm.
Divide the volume by the two known dimensions: 180 ÷ (9 × 5) = 180 ÷ 45 = 4 cm for the missing width.
9. A toolbox is 15 in × 8 in × 6 in. Its volume is 720 in³.
Multiply 15 × 8 = 120, then 120 × 6 = 720 in³. That is how much space the toolbox can hold inside.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each container to its volume.
4 ft × 3 ft × 5 ft
→ 60 ft³
42 ft³
6 ft × 6 ft × 1 ft
→ 36 ft³
32 ft³
3 ft × 7 ft × 2 ft
→ 42 ft³
60 ft³
8 ft × 2 ft × 2 ft
→ 32 ft³
36 ft³
Correct matches: 4 ft × 3 ft × 5 ft → 60 ft³; 6 ft × 6 ft × 1 ft → 36 ft³; 3 ft × 7 ft × 2 ft → 42 ft³; 8 ft × 2 ft × 2 ft → 32 ft³.