To find the volume of a rectangular prism, the formula is given by:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]
For the original dimensions of the prism:
- Width = 3 meters
- Length = 4 meters
- Height = 2 meters
Calculating the original volume:
\[ \text{Volume} = 3 , \text{m} \times 4 , \text{m} \times 2 , \text{m} = 24 , \text{m}^3 \]
Now, if the prism is dilated using a scale factor of 4, each dimension is multiplied by this scale factor:
- New Width = \( 3 , \text{m} \times 4 = 12 , \text{m} \)
- New Length = \( 4 , \text{m} \times 4 = 16 , \text{m} \)
- New Height = \( 2 , \text{m} \times 4 = 8 , \text{m} \)
Now, we calculate the new volume using the new dimensions:
\[ \text{New Volume} = 12 , \text{m} \times 16 , \text{m} \times 8 , \text{m} \]
First, calculate the product of the width and length:
\[ 12 \times 16 = 192 \]
Now multiply this result by the height:
\[ 192 \times 8 = 1536 , \text{m}^3 \]
Thus, the volume of the rectangular prism after dilation is:
1,536 m³