Answer:
The ratio of their volumes is equal to [tex]\frac{216}{343}[/tex]
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
[tex]z^{3}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{6}{7}[/tex]
substitute
[tex](\frac{6}{7})^{3}=\frac{x}{y}[/tex]
[tex](\frac{216}{343})=\frac{x}{y}[/tex]
rewrite
[tex]\frac{x}{y}=(\frac{216}{343})[/tex] -----> the fraction is irreducible
