Answer
The number of times greater is the volume of its larger cylinder than the smaller cylinder is\[16\text{ times}\]
Work Step by Step
The volume of cylinder will be computed by multiplying the square of radius with the height and finally multiplying the resultant with the value of pie.
Compute the volume of the cylinder using the equation as shown below:
\[\begin{align}
& \text{Volume of the Cylinder (}V\text{)}=\pi {{r}^{2}}h \\
& =\left( \pi {{\left( 2\text{ in}\text{.} \right)}^{2}}\left( 3\text{ in} \right) \right) \\
& =12\pi \text{ i}{{\text{n}}^{\text{3}}}
\end{align}\]
Thus, the volume of the cylinder is \[12\pi \text{ i}{{\text{n}}^{\text{3}}}\]
Now, when the radius of the cylinder gets quadrupled, compute the volume of the cylinder using the equation as shown below:
Firstly compute the new radius using the equation as shown below:
\[\begin{align}
& \text{New radius}=4\times \text{Old radius} \\
& =\left( 4\times 2\text{ in}\text{.} \right) \\
& =8\text{ in}
\end{align}\]
Compute the value of cylinder as shown below:
\[\begin{align}
& \text{Volume of the Cylinder (}V\text{)}=\pi {{r}^{2}}h \\
& =\left( \pi {{\left( 8\text{ in}\text{.} \right)}^{2}}\left( 3\text{ in} \right) \right)\text{i}{{\text{n}}^{3}} \\
& =192\pi \text{ i}{{\text{n}}^{\text{3}}}
\end{align}\]
Now, compute the number of times greater is the volume of its larger cylinder than the smaller cylinder using the equation as shown below:
\[\begin{align}
& \text{Number of times}=\frac{\text{Volume of new cylinder}}{\text{Volume of old cylinder}} \\
& =\frac{192\text{ inche}{{\text{s}}^{\text{3}}}}{12\text{ inche}{{\text{s}}^{\text{3}}}} \\
& =16
\end{align}\]
