Question

if the rectangular prism (L = 18 m, W = 4 m, H = 5 m) is dilated using a scale factor of 1/2, what would be the volume of the dilated rectangular prism

Answer 1

To find the volume of a rectangular prism, you use the formula:

\[
\text{Volume} = L \times W \times H
\]

For the original rectangular prism with dimensions \( L = 18 \, \text{m} \), \( W = 4 \, \text{m} \), and \( H = 5 \, \text{m} \):

\[
\text{Volume}_{\text{original}} = 18 \, \text{m} \times 4 \, \text{m} \times 5 \, \text{m} = 360 \, \text{m}^3
\]

When you dilate the prism using a scale factor of \( \frac{1}{2} \), the new dimensions will be:

- New Length \( L' = 18 \times \frac{1}{2} = 9 \, \text{m} \)
- New Width \( W' = 4 \times \frac{1}{2} = 2 \, \text{m} \)
- New Height \( H' = 5 \times \frac{1}{2} = 2.5 \, \text{m} \)

Now we can calculate the volume of the dilated rectangular prism:

\[
\text{Volume}_{\text{dilated}} = L' \times W' \times H'
\]

\[
\text{Volume}_{\text{dilated}} = 9 \, \text{m} \times 2 \, \text{m} \times 2.5 \, \text{m} = 45 \, \text{m}^3
\]

Thus, the volume of the dilated rectangular prism is:

\[
\boxed{45 \, \text{m}^3}
\]