Answer
The ratio of the volume of the sphere having radius \[3\text{ inches}\]to the volume of sphere having radius \[6\text{ inches}\]is\[\frac{1}{8}\].
Work Step by Step
Compute the volume of the sphere having radius \[3\text{ inches}\]using the equation as shown below:
\[\begin{align}
& \text{Volume of the Sphere (}{{V}_{1}}\text{)}=\frac{4}{3}\pi {{r}^{3}} \\
& =\frac{4}{3}\left( \pi {{\left( 3 \right)}^{3}} \right)\text{ i}{{\text{n}}^{3}} \\
& =36\pi \text{ i}{{\text{n}}^{\text{3}}}
\end{align}\]
Again, compute the volume of the sphere having radius of \[3\text{ inches}\]using the equation as shown below:
\[\begin{align}
& \text{Volume of the Sphere (}{{V}_{2}}\text{)}=\frac{4}{3}\pi {{r}^{3}} \\
& =\frac{4}{3}\left( \pi {{\left( 6 \right)}^{3}} \right)\text{ i}{{\text{n}}^{3}} \\
& =288\pi \text{ i}{{\text{n}}^{\text{3}}}
\end{align}\]
Now, compute the required ratio using the equation as shown below:
\[\begin{align}
& \text{Ratio}=\frac{{{V}_{1}}}{{{V}_{2}}} \\
& =\frac{36\pi \text{ i}{{\text{n}}^{3}}}{288\pi \text{ i}{{\text{n}}^{3}}} \\
& =\frac{36}{288} \\
& =\frac{1}{8}
\end{align}\]
