Question

If the radius of a cylinder is reduced by $50\%$, then volume of the cylinder will get reduced by

• A. 25%
• B. 50%
• C. 75%
• D. 40%

Answer 1

The correct option is C

75%

Let the radius of the old cylinder be $R$ and that of the new cylinder be $r.$

Then, $r=\frac{R}{2}$

Volume of old cylinder $=\pi R^{2}h$

Volume of new cylinder $=\pi r^{2}h$

$=\pi \times {\left(\frac{R}{2}\right)}^2\times h=\frac{\pi R^{2}h}{4}$

Hence, reduction in volume $=\pi R^{2}h-\frac{\pi R^{2}h}{4}$

$=\frac{3}{4}\pi R^{2}h$

$\therefore$ percentage reduction $=\frac{\frac{3}{4}\pi R^{2}h}{\pi R^{2}h}\times 100$

$=\frac{3}{4}\times 100=75\%$