Answer
\[\frac{1}{27}\]
Work Step by Step
Compute the volume of the sphere having radius 3 inches using the equation as shown below:
\[\begin{align}
& \text{Volume of the Sphere (}{{V}_{1}}\text{)}=\frac{4}{3}\pi {{r}^{3}} \\
& =\frac{4}{3}\left( \pi {{\left( 3 \right)}^{3}} \right)\text{i}{{\text{n}}^{3}} \\
& =36\pi \text{ i}{{\text{n}}^{3}}
\end{align}\]
Again, compute the volume of the sphere having radius 9 inches using the equation as shown below:
\[\begin{align}
& \text{Volume of the Sphere (}{{V}_{2}}\text{)}=\frac{4}{3}\pi {{r}^{3}} \\
& =\frac{4}{3}\left( \pi {{\left( 9 \right)}^{3}} \right)\text{i}{{\text{n}}^{3}} \\
& =972\pi \text{ i}{{\text{n}}^{3}}
\end{align}\]
Now, compute the required ratio using the equation as shown below:
\[\begin{align}
& \text{Ratio}=\frac{{{V}_{1}}}{{{V}_{2}}} \\
& =\frac{36\pi \text{ i}{{\text{n}}^{3}}}{972\pi \text{ i}{{\text{n}}^{3}}} \\
& =\frac{36}{972} \\
& =\frac{1}{27}
\end{align}\]
