Question

The radius of the base and height of a right circular cylinder are each increased by $20\%$. The volume of the cylinder will be increased by:

• A. $40\%$
• B. $60\%$
• C. $72.8\%$
• D. $96\%$

Answer 1

The correct option is C $72.8\%$

Let the radius of the original cylinder $=r$ cm and height $=h$ cm
Original volume $=\pi r^{2}h$
New Radius after increase $=\frac{120}{100}r=\frac{6}{5}r$
New height after increase $=\frac{120}{100}h=\frac{6}{5}h$
Now, new volume of the cylinder $=\pi \times {\left(\frac{6}{5}r\right)}^2\times \frac{6}{5}h=\frac{216\pi r^2}{125}h$

% decrease $=\frac{\text{Change in volume}}{\text{Original volume}}=\frac{\frac{216\pi r^2}{125}h-\pi r^{2}h}{\pi r^{2}h}\times 100$

$=\frac{\frac{91\pi r^2}{125}h}{\pi r^{2}h}\times 100$

$=\frac{91}{125}\times 100=72.8\%$