To determine the volume of the rectangular prism after dilation, we can first calculate the volume of the original prism and then apply the scale factor.
The volume \( V \) of a rectangular prism is calculated using the formula: \[ V = \text{length} \times \text{width} \times \text{height} \]
For the original prism:
- Length = 4 meters
- Width = 3 meters
- Height = 2 meters
Plugging in the values: \[ V = 4 , \text{m} \times 3 , \text{m} \times 2 , \text{m} = 24 , \text{m}^3 \]
Now, when the rectangular prism is dilated using a scale factor of 4, the new dimensions will be:
- New Length = \( 4 \times 4 = 16 \) meters
- New Width = \( 4 \times 3 = 12 \) meters
- New Height = \( 4 \times 2 = 8 \) meters
Now we can calculate the volume of the dilated prism: \[ V_{dilated} = \text{new length} \times \text{new width} \times \text{new height} \]
Substituting the new dimensions: \[ V_{dilated} = 16 , \text{m} \times 12 , \text{m} \times 8 , \text{m} \]
Calculating { \[ V_{dilated} = 16 \times 12 = 192 , \text{m}^2 \] \[ 192 \times 8 = 1536 , \text{m}^3 \]
Therefore, the volume of the rectangular prism after dilation is: 1,536 m³.
The correct response is thus: 1,536 m3 or 1,536 m cubed.