Answer:
The volume of the larger rectangular prism is \(648\ cm^{3}\)
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z-----> the scale factor
x-----> the volume of the larger rectangular prism
y-----> the volume of the smaller rectangular prism
\(z^{3}=\frac{x}{y}\)
In this problem we have
\(z=\frac{12}{4}=3\) ---> the scale factor is equal to the ratio of its corresponding sides
\(y=24\ cm^{3}\)
substitute and solve for x
\(3^{3}=\frac{x}{24}\)
\(x=27*24=648\ cm^{3}\)
