Two nonoverlapping prisms measure 6 × 4 × 2 cm and 3 × 4 × 5 cm. Find the combined volume.
- First prism: 6 × 4 × 2 = 48 cubic cm.
- Second prism: 3 × 4 × 5 = 60 cubic cm.
- Add the two parts: 48 + 60.
Answer: 108 cubic cm
Volume of Composite Figures Worksheets
Decompose two joined rectangular prisms, multiply each set of dimensions, and add their volumes. Diagrams are not to scale.
Learn the skill
Finding the volume of composite figures
A composite solid can be split into simpler solids. For a figure made of nonoverlapping rectangular prisms, find each prism’s length × width × height, then add the volumes. Every measurement must use the same unit.
A method you can use
- Mark a split that leaves two rectangular prisms. Each part needs three dimensions.
- Find missing lengths by subtracting aligned lengths from a total; do not guess from the drawing.
- Multiply within each prism, add the results, and label the answer in cubic units.
Worked examples
A solid fills a 10 × 4 × 6 cm box except for a 3 × 4 × 2 cm rectangular notch. Find its volume.
- The full box would hold 10 × 4 × 6 = 240 cubic cm.
- The empty notch is 3 × 4 × 2 = 24 cubic cm.
- Subtract the empty part: 240 − 24.
Answer: 216 cubic cm
A base prism is 8 × 3 × 2 cm. A prism on top has length 5 cm, width 3 cm, and reaches a total height of 6 cm from the bottom. Find the solid’s volume.
- The upper prism’s own height is 6 − 2 = 4 cm.
- Base volume: 8 × 3 × 2 = 48. Upper volume: 5 × 3 × 4 = 60.
- The two prisms share a face but no volume; add 48 + 60.
Answer: 108 cubic cm
Why two different splits can give the same volume
A solid consists of a 6 × 4 × 2 cm base with a 2 × 4 × 3 cm prism on top at one end. Can you find its volume in two ways?
See the reasoning
A horizontal split gives 6 × 4 × 2 + 2 × 4 × 3 = 48 + 24 = 72 cubic cm.
A vertical split gives a tall 2 × 4 × 5 prism and a short 4 × 4 × 2 prism: 40 + 32 = 72 cubic cm.
Both splits cover exactly the same solid without gaps or overlaps. If your answers differ, inspect which dimensions belong to each part.
Try a transfer problem
An 8 × 3 × 2 cm base has a 3 × 3 × 4 cm prism on top at one end. Use a vertical split to find the total volume.
Check the solution
The tall part is 3 × 3 × 6 = 54. The remaining short part is (8 − 3) × 3 × 2 = 30. Add 54 + 30 = 84.
84 cubic cm
Try it yourself
Solve these before opening the answers. The printable sets below give you more practice.
1. Two nonoverlapping prisms measure 4 × 3 × 2 cm and 2 × 3 × 5 cm. Find their total volume.
Show answer and explanation
54 cubic cm
The volumes are 24 and 30 cubic cm; 24 + 30 = 54.
2. A 6 × 5 × 4 cm block has a 2 × 5 × 1 cm notch removed. Find the remaining volume.
Show answer and explanation
110 cubic cm
Subtract the notch: 120 − 10 = 110 cubic cm.
Before you begin
Multiply whole numbers and find the volume of a rectangular prism: length × width × height.
Choose your level
- Easy: Add volumes of two prisms with small whole-number dimensions.
- Medium: Use larger dimensions and show both volume calculations.
- Hard: Use total volume to find the missing height of one prism.
Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.
Preview and print an easy set
Try six questions below, or choose a full set at your level.
1
Two prisms touch without overlapping. Left: 3 × 5 × 7 cm. Right: 4 × 5 × 5 cm. Find the total volume.
2
Two prisms touch without overlapping. Left: 3 × 5 × 8 cm. Right: 8 × 5 × 2 cm. Find the total volume.
3
Two prisms touch without overlapping. Left: 3 × 5 × 9 cm. Right: 5 × 5 × 6 cm. Find the total volume.
4
Two prisms touch without overlapping. Left: 6 × 3 × 10 cm. Right: 8 × 3 × 5 cm. Find the total volume.
5
Two prisms touch without overlapping. Left: 3 × 2 × 5 cm. Right: 2 × 2 × 3 cm. Find the total volume.
6
Two prisms touch without overlapping. Left: 5 × 4 × 10 cm. Right: 6 × 4 × 3 cm. Find the total volume.
Answer Key
1. 205 cm³ (105 + 100)2. 200 cm³ (120 + 80)3. 285 cm³ (135 + 150)4. 300 cm³ (180 + 120)5. 42 cm³ (30 + 12)6. 272 cm³ (200 + 72)