To determine the volume of a rectangular prism, you can use the formula:
\[ \text{Volume} = \text{width} \times \text{length} \times \text{height} \]
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Original dimensions of the rectangular prism:
- Width = 3 meters
- Length = 4 meters
- Height = 2 meters
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Calculate the original volume: \[ \text{Volume}_{\text{original}} = 3 , \text{m} \times 4 , \text{m} \times 2 , \text{m} = 24 , \text{m}^3 \]
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Dilation with a scale factor of 4: When dilated by a scale factor \( k \), each dimension is multiplied by \( k \). Therefore, the new dimensions will be:
- New Width = \( 3 , \text{m} \times 4 = 12 , \text{m} \)
- New Length = \( 4 , \text{m} \times 4 = 16 , \text{m} \)
- New Height = \( 2 , \text{m} \times 4 = 8 , \text{m} \)
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Calculate the volume of the dilated prism: \[ \text{Volume}_{\text{dilated}} = 12 , \text{m} \times 16 , \text{m} \times 8 , \text{m} = 1536 , \text{m}^3 \]
Thus, the volume of the rectangular prism after dilation by a scale factor of 4 is 1,536 m³.
The correct response is 1,536 m³.