Answer:
The volume of the resulting solid is eight times smaller than the volume of the original solid
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 resulting solid
y-----> the volume of the original solid
so
[tex]z^{3}=\frac{x}{y}[/tex]
In this problem we have
[tex]z=\frac{1}{2}[/tex]
substitute
[tex](\frac{1}{2})^{3}=\frac{x}{y}[/tex]
[tex](\frac{1}{8})=\frac{x}{y}[/tex]
[tex]y=8x[/tex]
The volume of of the original solid is eight times larger than the volume of the resulting solid
or
[tex]x=(1/8)y[/tex]
The volume of the resulting solid is eight times smaller than the volume of the original solid
