To determine the volume of the rectangular prism after dilation, we start with the original dimensions and then apply the scale factor.
Original dimensions of the prism:
- Width = 3 m
- Length = 4 m
- Height = 2 m
Volume of the original prism: \[ \text{Volume} = \text{Width} \times \text{Length} \times \text{Height} = 3 , \text{m} \times 4 , \text{m} \times 2 , \text{m} = 24 , \text{m}^3 \]
Applying the dilation with a scale factor of 4: The new dimensions after dilation will be:
- New width = 3 m × 4 = 12 m
- New length = 4 m × 4 = 16 m
- New height = 2 m × 4 = 8 m
Volume of the dilated prism: \[ \text{New Volume} = \text{New Width} \times \text{New Length} \times \text{New Height} = 12 , \text{m} \times 16 , \text{m} \times 8 , \text{m} \]
Calculating the new volume: \[ 12 \times 16 = 192 \] \[ 192 \times 8 = 1536 \]
Thus, the volume of the rectangular prism after dilation is: \[ \text{New Volume} = 1536 , \text{m}^3 \]
So the correct response is: 1,536 m3 or 1,536 m cubed.