To determine the new volume of a triangular prism after dilation with a scale factor of 3, you need to know that when an object is dilated by a scale factor \( k \), the volume of the object is multiplied by \( k^3 \).
If \( V \) is the original volume of the triangular prism, then the new volume \( V' \) after dilating with a scale factor of 3 is given by:
\[ V' = k^3 \times V \]
In this case, \( k = 3 \), so:
\[ V' = 3^3 \times V = 27 \times V \]
Since we are not given the original volume \( V \), we can derive the new volume based on the scale factor alone.
Assuming the original volume of the prism was \( V = 1 \) m³ (for the sake of establishing a base calculation), the new volume would be:
\[ V' = 27 \times 1 = 27 \text{ m}^3 \]
However, since the original volume is not provided in your question, we cannot get a definitive numerical answer. But if you already have a particular original volume (as in any of the options), you would multiply that volume by 27 to find the new volume post-dilation.
If the question intends for the answers provided to be calculated based on certain assumptions (for example, if \( V \) was originally around \( 1,008 \) m³, the new volume would be \( 27 \times 1,008 = 27,216 \) m³, which is one of the options you've listed.
Thus, please confirm the original volume provided if necessary, but based on the options available and numerical logic, the newly estimated volume with a factor of \( 27 \) from an original base volume won't apply directly.
Nevertheless, if you meant to take one of the given options as the starting point, then:
- From \( 1,008 \text{ m}^3 \), the new volume would be = \( 27 \times 1,008 = 27,216 \text{ m}^3 \).
So the correct answer would be \( О 27,216 \text{ m}^3 \).