Question

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

• A. $4$ times
• B. $3$ times
• C. $6$ times
• D. $8$ times

Answer 1

The correct option is D

$8$ times

9Find dimensions of the cone

The volume of cone $\left(v\right)$$=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}$

If the radius and height of the cone gets doubled, then $R=2r$ and $H=2h$

Now, the new volume of the cone will be

$V=\frac{1}{3}\mathrm{\pi }{\left(2r\right)}^2\left(2h\right)$

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

$\Rightarrow V=8\left(\frac{1}{3}\pi r^{2}h\right)$

$\Rightarrow V=8v$

Hence, the volume of the cone will be increased by 8 times if the radius and height of the cylinder gets doubled.