Question

If the height of a cone is doubled then its volume is increased by

• A. 25%
• B. 50%
• C. 100%
• D. 150%

Answer 1

The correct option is C 100%

Let the radius of the cone be r and height be h

$\therefore$ Volume of the cone$=\frac{1}{3}\pi r^{2}h$

If the height of the cone is doubled then the height of the cone be 2h

$\therefore$ Volume of the cone$=\frac{1}{3}\pi r^{2}2h$

percentage change in voulume$\Rightarrow \frac{\frac{1}{3}\pi r^{2}2h-\frac{1}{3}\pi r^{2}h}{\frac{1}{3}\pi r^{2}h}\times 100$

$\Rightarrow \frac{\frac{1}{3}\pi r^2(2h-h)}{\frac{1}{3}\pi r^{2}h}\times 100$

$\Rightarrow \frac{\frac{1}{3}\pi r^{2}h}{\frac{1}{3}\pi r^{2}h}\times 100=100$%