Question

similar figures and volume quick check
use the image to answer the question
determine the volume of the rectangular prism if it were dilated using a scale factor of 4.
(1 point)
1,536 m³
96 m³
6 m³
384 m³

Explanation:

Step1: Find the volume of the original prism

The volume formula for a rectangular prism is \(V = l\times w\times h\). Given \(l = 4m\), \(w=3m\), \(h = 2m\), then \(V_{original}=4\times3\times2=24m^{3}\).

Step2: Use the scale - factor for volume

When a three - dimensional figure is dilated by a scale factor \(k\), the volume of the new figure \(V_{new}\) is related to the volume of the original figure \(V_{original}\) by the formula \(V_{new}=V_{original}\times k^{3}\). Here \(k = 4\), so \(V_{new}=24\times4^{3}\).
Since \(4^{3}=4\times4\times4 = 64\), then \(V_{new}=24\times64\).
\(24\times64=(20 + 4)\times64=20\times64+4\times64=1280+256 = 1536m^{3}\).

Answer:

\(1536m^{3}\)