Question

5 m
18 m
4 m

If the rectangular prism is dilated using a scale factor of 1/2, what would be the volume of the dilated rectangular prism?

___ m^3

Answer 1

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

\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]

For the original rectangular prism, we have the dimensions:
- Length = 5 m
- Width = 18 m
- Height = 4 m

Calculating the original volume:

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

When the rectangular prism is dilated with a scale factor of \( \frac{1}{2} \), each dimension is multiplied by \( \frac{1}{2} \):

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

Next, we find the volume of the dilated rectangular prism:

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

Calculating this step-by-step:

1. \( 2.5 \times 9 = 22.5 \)
2. \( 22.5 \times 2 = 45 \)

So the volume of the dilated rectangular prism is:

\[
\text{Volume}_{\text{dilated}} = 45 \, \text{m}^3
\]

Thus, the final answer is:

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