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)
6 m³
1,536 m³
384 m³
96 m³

Explanation:

Step1: Calculate the original volume

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

Step2: Use the scale - factor formula for volume

If the scale factor is \(k\), the volume of the dilated figure \(V_{dilated}=V_{original}\times k^{3}\). Here \(k = 4\), then \(V_{dilated}=24\times4^{3}\).
Since \(4^{3}=4\times4\times4 = 64\), then \(V_{dilated}=24\times64\).
\(24\times64=(20 + 4)\times64=20\times64+4\times64=1280+256 = 1536m^{3}\).

Answer:

\(1,536m^{3}\)