Volume of Rectangular Prisms — Answer Key
Part A: Fill in the Blank
Write the missing word or number on each line.
1. To find the volume of an L-shaped figure, split it into two rectangular prisms and add their volumes.
An L-shaped figure is not a single rectangular prism, so you break it into two separate rectangular prisms, find each volume, and add them together.
2. A prism is 7 cm × 4 cm × 6 cm. Its volume is 168 cm³.
Multiply all three dimensions: 7 × 4 = 28, then 28 × 6 = 168 cm³.
3. A box has a volume of 150 m³. If the base area is 30 m², the height is 5 m.
Using V = B × h, divide 150 m³ by the base area of 30 m² to get h = 5 m.
4. Prism A is 4×5×3 cm and Prism B is 2×5×3 cm. Together they have a volume of 90 cm³.
Find each volume separately: Prism A is 4 × 5 × 3 = 60 cm³ and Prism B is 2 × 5 × 3 = 30 cm³, so together they total 60 + 30 = 90 cm³.
5. A cube with edge length 3 ft has a volume of 27 ft³.
A cube has equal edges, so its volume is 3 × 3 × 3 = 27 ft³.
6. If Prism X has volume 200 cm³ and Prism Y has volume 180 cm³, Prism X holds 20 cm³ more.
Subtract the two volumes: 200 − 180 = 20 cm³, so Prism X holds 20 cubic centimeters more than Prism Y.
7. A rectangular prism has a volume of 96 in³, a length of 8 in, and a width of 4 in. Its height is 3 in.
Divide the volume by the product of the known dimensions: 96 ÷ (8 × 4) = 96 ÷ 32 = 3 in.
8. The volume of a rectangular prism can also be found by multiplying the area of the base by the height.
The formula V = B × h works because the base area (B = l × w) tells you how many unit cubes fit in one layer, and the height tells you how many layers there are.
9. A prism 11 cm × 2 cm × 5 cm has a volume of 110 cm³.
Multiply 11 × 2 × 5: first 11 × 2 = 22, then 22 × 5 = 110 cm³.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each rectangular prism to its volume.
9 cm × 3 cm × 4 cm
→ 108 cm³
125 cm³
7 cm × 6 cm × 2 cm
→ 84 cm³
108 cm³
5 cm × 5 cm × 5 cm
→ 125 cm³
120 cm³
10 cm × 4 cm × 3 cm
→ 120 cm³
84 cm³
Correct matches: 9 cm × 3 cm × 4 cm → 108 cm³; 7 cm × 6 cm × 2 cm → 84 cm³; 5 cm × 5 cm × 5 cm → 125 cm³; 10 cm × 4 cm × 3 cm → 120 cm³.