Answer:
The volume ratio of the enlarged prism to the original prism is equal to
[tex]27[/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 enlarged prism
y-----> the volume of the original prism
so
[tex]z^{3}=\frac{x}{y}[/tex]
we have
[tex]z=3[/tex]
[tex]y=24\ in^{3}[/tex]
substitute
[tex]3^{3}=\frac{x}{24}[/tex]
[tex]x=(27)(24)=648\ in^{3}[/tex] -----> volume of the enlarged prism
the volume ratio of the enlarged prism to the original prism is equal to
[tex]3^{3}=27[/tex]
Verify
[tex]\frac{648}{24}=27[/tex] -----> is correct
