To determine the volume of a rectangular prism, the formula is:
\[ V = L \times W \times h \]
For the original dimensions given:
- Length (L) = 4 m
- Width (W) = 3 m
- Height (h) = 2 m
Calculating the original volume:
\[ V = 4 , \text{m} \times 3 , \text{m} \times 2 , \text{m} = 24 , \text{m}^3 \]
If the prism is dilated using a scale factor of 4, the new dimensions will be:
- New Length (L') = \( 4 \times 4 = 16 , \text{m} \)
- New Width (W') = \( 3 \times 4 = 12 , \text{m} \)
- New Height (h') = \( 2 \times 4 = 8 , \text{m} \)
Now we can calculate the volume of the dilated rectangular prism:
\[ V' = L' \times W' \times h' = 16 , \text{m} \times 12 , \text{m} \times 8 , \text{m} \]
Calculating the new volume:
\[ V' = 16 \times 12 \times 8 = 1536 , \text{m}^3 \]
Thus, the volume of the dilated rectangular prism is \( \text{1536 m}^3 \).