Add Volumes of Non-Overlapping Prisms

Supplied materials

• Paper and a pencil; drawing and spoken explanations are welcome. An adult may read directions and options aloud.
• Supplied worked-case record: A solid has adjoining prisms 4×3×2 and 2×3×5 units with no interior overlap.
• All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.

Learn the idea

A solid can be decomposed into rectangular prisms with non-overlapping interiors. Compute each prism’s volume and add the results. Shared faces have no volume, but an overlapped block would be counted twice. The stated decomposition must include the full solid.

Calculate each supplied length × width × height product. Add the volumes because the exercise explicitly states no interior overlap. Check unit consistency and distinguish a shared face from an overlapped three-dimensional region.

Verify the supplied non-overlap condition. Do not add an extra amount for the shared joining face. Pattern the two solid parts differently and list each volume before adding.

1. Pattern the two solid parts differently and list each volume before adding.
2. Follow the worked example. Point to each number or shape feature and say what it tells you.
3. Calculate each supplied length × width × height product.
4. Try the question and then the three practice questions. Check your answers and explain any change you make.

Check your reasoning

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Take it further

Non-overlapping 5×4×2 and 3×2×6 prisms have total volume 76 cubic units.

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