Question

Determine the volume of the rectangular prism if it were dilated using a scale factor of 4. L = 4m W = 3m H = 2m(1 point) Responses 1,536 m3 1,536 m cubed 384 m3 384 m cubed 96 m3 96 m cubed 6 m3

Answer 1

To determine the volume of the rectangular prism after dilation with a scale factor of 4, we first need to calculate the original volume of the prism.

The volume \( V \) of a rectangular prism can be calculated using the formula:

\[
V = L \times W \times H
\]

Where:
- \( L \) = Length = 4 m
- \( W \) = Width = 3 m
- \( H \) = Height = 2 m

Calculating the original volume:

\[
V = 4 \, \text{m} \times 3 \, \text{m} \times 2 \, \text{m} = 24 \, \text{m}^3
\]

Now, when the prism is dilated using a scale factor of 4, the new dimensions will be:

- New length \( L' = 4 \times 4 = 16 \, \text{m} \)
- New width \( W' = 4 \times 3 = 12 \, \text{m} \)
- New height \( H' = 4 \times 2 = 8 \, \text{m} \)

Now, we calculate the new volume \( V' \) using the new dimensions:

\[
V' = L' \times W' \times H' = 16 \, \text{m} \times 12 \, \text{m} \times 8 \, \text{m}
\]

Calculating this step-by-step:

1. Calculate \( 16 \, \text{m} \times 12 \, \text{m} = 192 \, \text{m}^2 \)
2. Then calculate \( 192 \, \text{m}^2 \times 8 \, \text{m} = 1536 \, \text{m}^3 \)

Thus, the volume of the dilated rectangular prism is:

\[
\boxed{1536 \, \text{m}^3}
\]