Question

If the both the radius and height of a right circular cone are increased by 20%, its volume will be increased by:

• A. 40%
• B. 60%
• C. 72.8%
• D. 80%

Answer 1

The correct option is C

72.8%

Let the original radius and height of the cone be `r' and `h' respectively.

Then, original volume $=\frac{1}{3}\pi r^{2}h.$

New radius = $\frac{120}{100}r=\frac{6}{5}r,$

New height = $\frac{6}{5}h$

New volume $=\frac{1}{3}\pi \times {\left(\frac{6}{5}r\right)}^2\times \left(\frac{6}{5}h\right)=\frac{216}{125}\times \frac{1}{3}\pi r^{2}h$

Increase in volume $=\frac{91}{125}\times \frac{1}{3}\pi r^{2}h$

$\therefore$Increase % = $\left[\frac{\frac{91}{125}\times \frac{1}{3}\pi r^{2}h}{\frac{1}{3}\pi r^{2}h}\times 100\right]$

= 72.8%