To determine the volume of the new rectangular prism with a scale factor of 12, we need to know the volume of the original rectangular prism.
The formula for the volume of a rectangular prism is:
\[ V = \text{length} \times \text{width} \times \text{height} \]
If the volume of the original prism is \( V_{\text{original}} \), the volume of the new prism after applying the scale factor can be calculated using the cube of the scale factor. The volume scales by the cube of the scale factor, so:
\[ V_{\text{new}} = V_{\text{original}} \times (\text{scale factor})^3 \]
Given that the scale factor is 12, we calculate \( 12^3 \):
\[ 12^3 = 12 \times 12 \times 12 = 1728 \]
Thus, the formula for the new volume becomes:
\[ V_{\text{new}} = V_{\text{original}} \times 1728 \]
Since we don't have the value of \( V_{\text{original}} \), we can't compute \( V_{\text{new}} \) directly. However, if we assume \( V_{\text{original}} \) is provided, we can determine \( V_{\text{new}} \).
Here’s how the options might relate to different possible \( V_{\text{original}} \):
- If \( V_{\text{original}} = \frac{15}{1728} \) cm³, then \( V_{\text{new}} = 15 \) cm³.
- If \( V_{\text{original}} = \frac{120}{1728} \) cm³, then \( V_{\text{new}} = 120 \) cm³.
- If \( V_{\text{original}} = \frac{30}{1728} \) cm³, then \( V_{\text{new}} = 30 \) cm³.
- If \( V_{\text{original}} = \frac{60}{1728} \) cm³, then \( V_{\text{new}} = 60 \) cm³.
Please check the question for the volume of the original rectangular prism, as without that information, we cannot select the correct volume among the given options.
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