Two blocks of 60 cm³ and 24 cm³ are joined without overlap.
- Add the volumes: 60 + 24 = 84 cm³.
- Do not add an internal overlap if the pieces overlap.
Composite solids & design decisions
Break a complex shape into manageable solids.
Break the solid apart
Choose which exposed surfaces and volumes to add or subtract, and justify a design.
Find the volume of non-overlapping pieces and add them. For a removed piece, subtract its volume from the original solid.
Explore the dimensions
Predict first, then change one dimension. Diagrams are schematic; results use the entered values. Rounded values are marked ≈.
Shared faces are internal
For the exterior surface area of joined solids, exclude the surfaces hidden where they touch. Draw and label exposed faces; count each once.
Compare sizes carefully
A volume ratio compares capacities; a surface-area ratio compares surface amounts. Neither alone proves two shapes physically fit: orientation, dimensions and material thickness matter.
Worked examples
A box has external dimensions 5 × 4 × 3 cm and no lid.
- Material surface area without tabs = 5×4 + 2(5×3) + 2(4×3) = 74 cm².
- An internal capacity calculation needs internal dimensions; material thickness matters.
Guided Practice
A 40 cm³ block has a 6 cm³ non-overlapping piece removed. What volume remains?
A first hint
Subtract the removed volume.
Compare your reasoning
40 − 6 = 34 cm³.
Practice
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
0 of 8 questions completed
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Connections
Two nesting boxes have a 70% volume ratio. Why is that not enough to establish that they fit?
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