Answer:
The volume of the larger rectangular prism is [tex]648\ cm^{3}[/tex]
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
[tex]z^{3}=\frac{x}{y}[/tex]
In this problem we have
[tex]z=\frac{12}{4}=3[/tex] ---> the scale factor is equal to the ratio of its corresponding sides
[tex]y=24\ cm^{3}[/tex]
substitute and solve for x
[tex]3^{3}=\frac{x}{24}[/tex]
[tex]x=27*24=648\ cm^{3}[/tex]
