To find the volume of the rectangular prism before dilation, we use the formula for the volume of a rectangular prism:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]
Substituting the given dimensions of the prism (length = 18 m, width = 4 m, height = 5 m):
\[ \text{Volume} = 18 , \text{m} \times 4 , \text{m} \times 5 , \text{m} = 360 , \text{m}^3 \]
Now, when the prism is dilated using a scale factor of \( \frac{1}{2} \), the new dimensions will be:
\[ \text{New length} = 18 , \text{m} \times \frac{1}{2} = 9 , \text{m} \] \[ \text{New width} = 4 , \text{m} \times \frac{1}{2} = 2 , \text{m} \] \[ \text{New height} = 5 , \text{m} \times \frac{1}{2} = 2.5 , \text{m} \]
Now, we can calculate the volume of the dilated rectangular prism:
\[ \text{Dilated Volume} = \text{new length} \times \text{new width} \times \text{new height} \] \[ \text{Dilated Volume} = 9 , \text{m} \times 2 , \text{m} \times 2.5 , \text{m} = 45 , \text{m}^3 \]
Thus, the volume of the dilated rectangular prism is \( \boxed{45} , \text{m}^3 \).
1 answer