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 solid, split it into two rectangular prisms and add their volumes.
Composite solids can be broken into simpler shapes. Add their individual volumes for the total.
2. Prism A is 4×3×2 cm and Prism B is 5×3×2 cm. The combined volume is 54 cm³.
Prism A: 4×3×2=24. Prism B: 5×3×2=30. Total: 24+30=54 cm³.
3. A block is 10×6×4 cm with a 3×2×4 cm notch cut out. The remaining volume is 216 cm³.
Full block: 10×6×4=240. Notch: 3×2×4=24. Remaining: 240−24=216 cm³.
4. Two identical prisms each 2×3×5 in are stacked. The total volume is 60 in³.
One prism: 2×3×5=30 in³. Two prisms: 30×2=60 in³.
5. A T-shaped solid has a top piece 8×2×3 cm and a base 4×2×5 cm. Total volume is 88 cm³.
Top: 8×2×3=48. Base: 4×2×5=40. Total: 48+40=88 cm³.
6. When a hole is cut from a solid, we subtract the hole's volume from the solid's volume.
Remove the hole's volume from the whole solid: remaining = whole − hole.
7. A 6×6×6 cm cube has a 2×2×6 cm tunnel cut through it. The remaining volume is 192 cm³.
Cube: 6×6×6=216. Tunnel: 2×2×6=24. Remaining: 216−24=192 cm³.
8. Prism A is 3×4×5 m and Prism B is 3×4×3 m. Together their volume is 96 m³.
Prism A: 3×4×5=60. Prism B: 3×4×3=36. Total: 60+36=96 m³.
9. A step shape has a bottom layer 10×4×2 cm and a top layer 6×4×2 cm. Its volume is 128 cm³.
Bottom: 10×4×2=80. Top: 6×4×2=48. Total: 80+48=128 cm³.
Part B: Matching
Match each item on the left to the correct answer on the right.
1. Match each item to its correct answer.
Bottom 8×5×3 + Top 4×5×2
→ 160 cm³
84 cm³
Solid 7×4×6 − Hole 2×2×6
→ 144 cm³
90 cm³
Two stacked: 3×3×4 and 3×3×6
→ 90 cm³
144 cm³
Bottom 6×4×2 + Top 3×4×3
→ 84 cm³
160 cm³
8×5×3+4×5×2=120+40=160(idx3); 7×4×6−2×2×6=168−24=144(idx2); 3×3×4+3×3×6=36+54=90(idx1); 6×4×2+3×4×3=48+36=84(idx0)