Question

similar figures and volume quick check
use the image to answer the question.
if the triangular prism were dilated using a scale factor of 3, what would be the new volume?
(1 point)
27,216 m³
9,072 m³
112 m³
1,008 m³

Explanation:

Step1: Calculate the original volume

The formula for the volume of a triangular prism is \(V = \frac{1}{2}bh\times l\), where \(b = 7\)m (base of the triangle), \(h = 8\)m (height of the triangle), and \(l=12\)m (length of the prism).

$$
LATEXBLOCK0
$$

Step2: Use the scale - factor property for volume

When a three - dimensional figure is dilated by a scale factor \(k\), the new volume \(V_{new}=k^{3}V_{original}\). Here \(k = 3\).

$$
LATEXBLOCK1
$$

Answer:

\(9,072\space m^{3}\)