Question

If the height and radius of a cone are doubled, then the value of the cone becomes:

• A. $2$ times
• B. $4$ times
• C. $6$ times
• D. $8$ times

Answer 1

The correct option is D $8$ times

Let the radius of the cone=r cm

Height of the cone=h cm

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

If the height and radius of a cone are doubled then

Radius of the cone=2r cm

Height of the cone=2h cm

$\therefore$New volume$=\pi (2r{)}^2\frac{2h}{3}$

$\Rightarrow \pi 4r^2\times \frac{2h}{3}$

$\Rightarrow 8\pi r^2\frac{h}{3}$

Hence the new volume is 8 times of old volume.