Question

determine the volume of the rectangular prism (L = 4 m, W = 3 m, h = 2 m) if it were dilated using a scale factor of 4

Answer 1

To determine the volume of a rectangular prism, the formula is:

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

For the original dimensions given:
- Length (L) = 4 m
- Width (W) = 3 m
- Height (h) = 2 m

Calculating the original volume:

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

If 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') = \( 3 \times 4 = 12 \, \text{m} \)
- New Height (h') = \( 2 \times 4 = 8 \, \text{m} \)

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

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

Calculating the new volume:

\[
V' = 16 \times 12 \times 8 = 1536 \, \text{m}^3
\]

Thus, the volume of the dilated rectangular prism is \( \text{1536 m}^3 \).