Question

If the rectangular prism is dilated using a scale factor of 12 , what would be the volume of the dilated rectangular prism? (1 point)
4, 18, 5

Answer 1

To find the volume of a dilated rectangular prism, you first need to know the volume of the original prism and then apply the scale factor to that volume.

The volume \( V \) of a rectangular prism can be calculated using the formula:
\[
V = \text{length} \times \text{width} \times \text{height}
\]

If the original volume is \( V_0 \), then when a dilatation is applied with a scale factor \( k \), the volume of the new, dilated prism \( V \) can be calculated using the following equation:
\[
V = k^3 \times V_0
\]
where \( k \) is the scale factor.

In this case, since the scale factor \( k = 12 \), we have:
\[
k^3 = 12^3 = 1728
\]

Now, if the original volume \( V_0 \) were provided, you would multiply that volume by 1728 to find the volume of the dilated prism. However, since you haven't provided the original volume, I can't give you an exact numerical answer for the volume of the dilated rectangular prism.

To summarize:
- If you know the original volume \( V_0 \), the dilated volume would be \( 1728 \times V_0 \).
- If the original volume were one of the provided options (4, 18, or 5), you would calculate accordingly:
- For \( V_0 = 4 \): \( 1728 \times 4 = 6912 \)
- For \( V_0 = 18 \): \( 1728 \times 18 = 31104 \)
- For \( V_0 = 5 \): \( 1728 \times 5 = 8640 \)

Please verify the original volume if you are looking for an exact answer.