Let's analyze each statement based on the information provided about the prism.
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The middle layer of cubes is missing 7 unit cubes.
- True. This is explicitly stated in the problem description.
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There are 9 unit cubes stacked in the prism.
- Based on the information given, we know there are 7 unit cubes hidden from view and 7 missing from the middle layer. Assuming the missing cubes are part of the total count, the total would be the sum of the visible cubes plus the hidden cubes and the missing cubes. If we only know there are 7 hiding and 7 missing, we can't confidently say there are 9 unit cubes stacked in total without further details. So, this statement cannot be definitively declared true or false based on the provided details.
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There are 7 unit cubes that are hidden from view inside the prism.
- True. This is also explicitly stated in the problem description.
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The volume of the prism can be found by 12 times 3 because there are 12 cubes in each layer and there are 3 layers of cubes.
- False. The volume of a rectangular prism is given by the formula \( \text{Volume} = \text{length} \times \text{width} \times \text{height} \). In this case, the volume of the prism would be \( 4 \times 3 \times 3 = 36 \text{ cubic units} \). The statement about 12 cubes in each layer doesn't hold valid without additional context showing that 12 cubes are actually arranged per layer.
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The volume of the prism can be found by doubling the number of cubes in the prism because it is half full.
- False. The total volume of the prism is constant regardless of how full it appears; it does not change based on how many cubes are present or the observed fullness. Hence, we cannot simply double the count of cubes seen to determine volume accurately.
In summary, the true statements are:
- The middle layer of cubes is missing 7 unit cubes.
- There are 7 unit cubes that are hidden from view inside the prism.
7 answers