Question

If the radius of a right circular cylinder is decreased by $50\%$ and its height is increased by $60\%$, its volume will be decreased by:

• A. $10\%$
• B. $60\%$
• C. $40\%$
• D. $20\%$

Answer 1

The correct option is B $60\%$

Let the radius of the original cylinder $=r$ cm and height $=h$ cm

$\therefore$ Original volume = $\pi r^{2}h$

Then, radius after decrease $=\frac{r}{2}$ and the height after increase $=\frac{160}{100}h=\frac{8}{5}h$

$\therefore$ New volume = $\pi {\left(\frac{r}{2}\right)}^2\times \frac{8}{5}h$

$\therefore$ New volume $=\pi {\left(\frac{r}{2}\right)}^2\times \frac{8}{5}h$

$=\pi \times \frac{r^2}{4}\times \frac{8h}{5}=\frac{2\pi r^{2h}}{5}$

$\therefore$ % decrease $=(\frac{\pi r^{2}h-2/5\pi r^{2}h}{\pi r^{2}h}\times 100)$

$=(\frac{\frac{3}{5}\pi r^{2}h}{\pi r^{2}h}\times 100)$ $=(\frac{3}{5}\times 100)$

$=60\%$