Question

If the radius of a cylinder reduces by 50% and its height increases by 50%, then volume of the cylinder will get reduced by

• A. 37.5%
• B. 50%
• C. 62.5%
• D. 75%

Answer 1

The correct option is C 62.5%

Let $(r,h)$ and $(r\text{'},h\text{'})$ be the radii and heights of original and new cylinders, respectively.
Now, radius is reduced by 50%.
$\Rightarrow r^{\prime }=r-50\text{\% of r}=r-\frac{r}{2}=\frac{r}{2}$....(i)
And, height is increased by 50%.
$\Rightarrow h^{\prime }=h+50\text{\% of h}=h+\frac{h}{2}=\frac{3h}{2}$ .....(ii)
$\therefore \text{Volume of new cylinder}=\pi (r^{\prime }{)}^2{h}^{\prime }$
$=\pi \times {\left(\frac{r}{2}\right)}^2\times \frac{3h}{2}$ [From (i) and (ii)]
$=\frac{3}{8}\pi r^{2}h$
$\therefore \text{Percentage reduced in volume}=\frac{(\pi r^{2}h-\frac{3}{8}\pi r^{2}h)}{\pi r^{2}h}\times 100$
$=(1-\frac{3}{8})\times 100$
$=\frac{5}{8}\times 100=62.5\text{\%}$
Therefore, the volume of the cylinder will be reduced by 62.5%.
Hence, the correct answer is option (c).