Answer:
the new volume of the prism is [tex]64[/tex] times the original volume
Step-by-step explanation:
we know that
If two figures are similar, then the scale factor elevated to the cube is equal to the ratio of its volumes
Let
z------> the scale factor
x------> the volume of the dilated prism
y------> the volume of the original prism
so
[tex]z^{3} =\frac{x}{y}[/tex]
In this problem we have
[tex]z=4[/tex]
substitute
[tex]4^{3} =\frac{x}{y}[/tex]
[tex]64=\frac{x}{y}[/tex]
[tex]x=64y[/tex]
that means-----> the new volume of the prism is [tex]64[/tex] times the original volume
