Answer:
The ratio of their volumes is equal to \(\frac{27}{64}\)
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
\(z^{3}=\frac{x}{y}\)
we have
\(z=\frac{3}{4}\)
substitute
\((\frac{3}{4})^{3}=\frac{x}{y}\)
\((\frac{27}{64})=\frac{x}{y}\)
therefore
The ratio of their volumes is equal to \(\frac{27}{64}\)
