Question

use the image to answer the question. determine the volume of the figure if it were dilated using a scale factor of 2 (1 point) cm³ check answer remaining attempts 3

Explanation:

Step1: Calculate the original volume

The formula for the volume of a triangular prism is \(V=\frac{1}{2}\times base\times height\times length\).
For the original prism, \(base = 8\space cm\), \(height=6\space cm\), \(length = 10\space cm\).
So, \(V_{original}=\frac{1}{2}\times8\times6\times10= 240\space cm^{3}\).

Step2: Apply the dilation formula

When a solid is dilated by a scale factor \(k\), the new volume \(V_{new}=k^{3}\times V_{original}\).
Here, \(k = 2\).
So, \(V_{new}=2^{3}\times240\).
\(V_{new}=8\times240 = 1920\space cm^{3}\).

Answer:

\(1920\)