Answer:
The volume ratio of Prism A to Prism B is [tex]\frac{729}{8}[/tex]
Step-by-step explanation:
Step 1
Find the scale factor
we know that
If two figures are similar, then the ratio of its surface areas is equal to the scale factor squared
Let
z-----> scale factor
x/y----> ratio of the surface area of Prism A to Prism B
so
[tex]z^{2}=\frac{x}{y}[/tex]
we have
[tex]\frac{x}{y}=\frac{81}{4}[/tex]
substitute
[tex]z^{2}=\frac{81}{4}[/tex]
[tex]z=\frac{9}{2}[/tex]
step 3
Find the volume ratio of Prism A to Prism B.
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-----> scale factor
x/y----> volume ratio of Prism A to Prism B
so
[tex]z^{3}=\frac{x}{y}[/tex]
we have
[tex]z=\frac{9}{2}[/tex]
substitute
[tex](\frac{9}{2})^{3}=\frac{x}{y}[/tex]
[tex](\frac{729}{8})=\frac{x}{y}[/tex]
