To find the volume of the new rectangular prism with a scale factor of 12, we first need to calculate the volume of the original rectangular prism.
The volume \( V \) of a rectangular prism is given by the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
For the original prism:
- Length = 5 m
- Width = 6 m
- Height = 4 m
Calculating the volume:
\[ V = 5 , \text{m} \times 6 , \text{m} \times 4 , \text{m} = 120 , \text{m}^3 \]
Now, since the scale factor is 12, the volume of the new prism will be scaled by the cube of the scale factor (because volume scales with the cube of linear dimensions).
Calculating the volume of the new prism:
\[ V_{\text{new}} = V_{\text{original}} \times (\text{scale factor})^3 \]
Substituting the values:
\[ V_{\text{new}} = 120 , \text{m}^3 \times (12)^3 \]
Calculating \( (12)^3 \):
\[ (12)^3 = 1728 \]
Now we can calculate the new volume:
\[ V_{\text{new}} = 120 , \text{m}^3 \times 1728 = 207360 , \text{m}^3 \]
Thus, the volume of the new rectangular prism is \( 207360 , \text{m}^3 \).
It seems that the options you provided (30 cm³, 60 cm³, 120 cm³, and 15 cm³) are much smaller than the actual volume. If you need the volume in cubic centimeters instead of cubic meters (1 m³ = 1,000,000 cm³), you can convert:
\[ 207360 , \text{m}^3 = 207360 \times 10^6 , \text{cm}^3 = 207360000000 , \text{cm}^3 \]
This indicates the responses provided do not match the actual calculations based on the volume and scale factor. Please check the scale factor or dimensions for consistency.