Question

use the image to answer the question.
if the rectangular prism is dilated using a scale factor of \\( \frac { 1 } { 2 } \\), what would be the volume of the dilated rectangular prism?
(1 point)
\\( \square \mathrm { m } ^ { 3 } \\)
check answer remaining attempts : 3

Explanation:

Step1: Calculate the original volume

The formula for the volume of a rectangular prism is \(V = l\times w\times h\). Given \(l = 18\space m\), \(w=4\space m\), \(h = 5\space m\), then \(V_{original}=18\times4\times5=360\space m^{3}\).

Step2: Apply the scale - factor

When a three - dimensional object is dilated with a scale factor \(k\), the volume of the new object \(V_{new}=k^{3}\times V_{original}\). Here \(k=\frac{1}{2}\), so \(V_{new}=(\frac{1}{2})^{3}\times360\).

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Answer:

\(45\)