Answer:
The volume of the similar prism is [tex]336\ 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 prism
y----> the volume of the smaller prism
so
[tex]z^{3}=\frac{x}{y}[/tex]
In this problem we have
[tex]z=2[/tex] -----> the scale factor
[tex]y=42\ cm^{3}[/tex]
substitute and solve for x
[tex]x=42(2^{3})=336\ cm^{3}[/tex]
