To find the volume of a rectangular prism, the formula is:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]
For the original dimensions of the rectangular prism:
- Height = 5 m
- Width = 4 m
- Length = 18 m
Calculating the original volume:
\[ \text{Volume} = 18 , \text{m} \times 4 , \text{m} \times 5 , \text{m} = 360 , \text{m}^3 \]
When the prism is dilated with a scale factor of \( \frac{1}{2} \), each dimension is multiplied by \( \frac{1}{2} \):
- New Height = \( 5 , \text{m} \times \frac{1}{2} = 2.5 , \text{m} \)
- New Width = \( 4 , \text{m} \times \frac{1}{2} = 2 , \text{m} \)
- New Length = \( 18 , \text{m} \times \frac{1}{2} = 9 , \text{m} \)
Now, calculating the volume of the dilated rectangular prism:
\[ \text{New Volume} = 9 , \text{m} \times 2 , \text{m} \times 2.5 , \text{m} \]
Calculating this step-by-step:
- \( 9 \times 2 = 18 \)
- \( 18 \times 2.5 = 45 \)
Thus, the volume of the dilated rectangular prism is:
\[ \text{New Volume} = 45 , \text{m}^3 \]
Therefore, the volume of the dilated rectangular prism is 45 m³.
1 answer