Choose the correct answer of the following question:

Let the base radius and height of the original cylinder be $r$ and $h$, respectively.

Also,

The radius of the new cylinder, $R=\frac{r}{2}$ and its height, $H=h$.

Now,

The ratio of the volume of the new cylinder to that of the original cylinder $=\frac{\text { Volume of the new cylinder }}{\text { Voilume of the original cylinder }}$

$=\frac{\pi r^{2} h}{\pi R^{2} H}$

$=\frac{\pi r^{2} h}{\pi\left(\frac{r}{2}\right)^{2} h}$

$=\frac{4 \pi r^{2} h}{\pi r^{2} h}$

$=\frac{4}{1}$

$=4: 1$

Hence, the correct answer is option (d).