Question

If the height of a cone is doubled then keeping the same radius, how much times the volume will increase?

Answer 1

Let the original volume of cone be $V_1$ and new volume be $V_2$.

Height of original cone is $h$, height of new cone is $2h$ and radius of base is $r$.

$\therefore V_1=\frac{1}{3}\pi r^{2}h$
When height is doubled then volume
$V_2=\frac{1}{3}\pi r^2\times 2h=2\times \frac{1}{3}\pi r^{2}h$

$\Rightarrow V_2=2\times V_1$
So, when height is doubled, the volume is also doubled.