To determine the volume of a dilated rectangular prism, you can follow these steps:
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Calculate the original volume of the prism. The volume (V) of a rectangular prism is given by the formula: \[ V = \text{length} \times \text{width} \times \text{height} \]
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Apply the scale factor to find the new dimensions. If the prism is dilated using a scale factor (k), the new dimensions will be: \[ \text{new length} = k \times \text{original length} \] \[ \text{new width} = k \times \text{original width} \] \[ \text{new height} = k \times \text{original height} \]
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Calculate the volume of the dilated prism using the new dimensions: \[ V_{\text{dilated}} = (\text{new length}) \times (\text{new width}) \times (\text{new height}) = k^3 \times V_{\text{original}} \]
Since the scale factor is 4, you will cube this factor when calculating the new volume: \[ k^3 = 4^3 = 64 \]
Thus, the new volume is: \[ V_{\text{dilated}} = 64 \times V_{\text{original}} \]
Without the original volume provided in your question, please calculate it using the dimensions given in the image (not shown here). Once you have that volume, multiply it by 64 to find the dilated volume.
From the answer choices provided, if the original volume was indeed 6 m³, then the dilated volume would be: \[ 64 \times 6 = 384 \text{ m}^3 \]
If the original volume was something else, adjust the calculation accordingly to find the correct answer from the options given.