Answer:
The ratio of their volumes is equal to [tex]\frac{27}{64}[/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 dilated figure
y-------> the volume of the original figure
so
[tex]z^{3}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{3}{4}[/tex]
substitute
[tex](\frac{3}{4})^{3}=\frac{x}{y}[/tex]
[tex](\frac{27}{64})=\frac{x}{y}[/tex]
therefore
The ratio of their volumes is equal to [tex]\frac{27}{64}[/tex]
