A metallic solid cone is melted to form a solid cylinder. If the height of the cone was 16 cm and the ratio of the radius of the cone to the cylinder is 3:2,  then the height of the cylinder is:

Let the height of the cylinder be h.

It is known that the volume of solids remains the same in case of the conversion of solids from one shape into another.

∴ Volume of the cylinder = Volume of the cone

$\Rightarrow {{\mathrm{\pi r}}_1}^{2}h=\frac{1}{3}{{\mathrm{\pi r}}_2}^2\times 16$

$\Rightarrow \mathrm{h}=\frac{16}{3}\times {\left(\frac{{\mathrm{r}}_2}{{\mathrm{r}}_1}\right)}^2$

$\Rightarrow h=\frac{16}{3}\times {\left(\frac{3}{2}\right)}^2$

$\Rightarrow h=12 \mathrm{cm}$

Hence, the height of the cylinder is 12 cm.