Calculate Volume from Full Unit-Cube Layers
Use the supplied whole-number prism dimensions to draw one layer.
About 20 minutes, plus any extended practice
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 prism is 6 units by 3 units by 4 units.
- All quantities and shape descriptions are supplied in the worked example and questions; no purchase or personal information is needed.
Learn the idea
Volume counts equal cubes filling a solid without gaps or overlap. A rectangular layer contains length times width unit cubes. Multiplying the layer count by the number of layers gives the volume. The three length dimensions create cubic units, which differ from area’s square units.
Use the supplied whole-number prism dimensions to draw one layer. Find its cube count, then multiply by the number of full layers. Check the result with the three-factor product length × width × height.
Count complete layers, including stated hidden layers. Area uses two dimensions; prism volume uses three. Draw one rectangular cube layer and record how many identical layers fill the solid.
- Draw one rectangular cube layer and record how many identical layers fill the solid.
- Follow the worked example. Point to each number or shape feature and say what it tells you.
- Use the supplied whole-number prism dimensions to draw one layer.
- Try the question and then the three practice questions. Check your answers and explain any change you make.
See the method in action
A prism is 6 units by 3 units by 4 units. Each layer has eighteen unit cubes and four layers contain 72. Thus volume is 6×3×4=72 cubic units. The layer’s eighteen square-unit base area is not the full solid’s volume by itself. Count complete layers, including stated hidden layers. Area uses two dimensions; prism volume uses three. Draw one rectangular cube layer and record how many identical layers fill the solid.
Check your reasoning
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Helpful tips
- Count complete layers, including stated hidden layers.
- Area uses two dimensions; prism volume uses three.
See the answer and explanation
24
Multiply cubes per layer by the full layer count. The result is 24.
Take it further
A 7×5×3 prism holds 105 cubic units.
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