Answer:
The ratio of their volumes is equal to \(\frac{216}{343}\)
Step-by-step explanation:
we know that
If two solids are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube
Let
z-----> the scale factor
x/y----> the ratio of its volumes
so
\(z^{3}=\frac{x}{y}\)
we have
\(z=\frac{6}{7}\)
substitute
\((\frac{6}{7})^{3}=\frac{x}{y}\)
\((\frac{216}{343})=\frac{x}{y}\)
rewrite
\(\frac{x}{y}=(\frac{216}{343})\) -----> the fraction is irreducible
