Question

If the radius of a right circular cylinder is increased by $50\%$ and height is decreased by $20\%$, then the percentage change in volume of cylinder is

• A. $40\%$
• B. $50\%$
• C. $60\%$
• D. $80\%$

Answer 1

The correct option is D $80\%$

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

height $=h$ cm

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


New Radius after increase $=\frac{150}{100}r=\frac{3}{2}r$

New height after decrease $=\frac{80}{100}h=\frac{4}{5}h$

Now, new volume of the cylinder $=\pi \times {\left(\frac{3r}{2}\right)}^2\times \frac{4}{5}h=\frac{9\pi r^2}{5}h$

% increase $=\frac{Changeinvolume}{Originalvolume}=\frac{dfrac9\pi r^{2}5h-pi{r}^{2}h}{\pi r^{2}h}\times 100=\frac{\frac{4\pi r^2}{5}h}{\pi r^{2}h}\times 100=\frac{4}{5}\times 100=80$ %