Choose the correct answer of the following question:
Question:

Choose the correct answer of the following question:

If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is

(a) 1 : 2                         (b) 2 : 1                         (c) 1 : 4                         (d) 4 : 1 

Solution:

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).

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