# A metallic cone of radius 12 cm and height 24 cm is melted and made into spheres of radius 2 cm each.

**Question:**

A metallic cone of radius 12 cm and height 24 cm is melted and made into spheres of radius 2 cm each. How many spheres are formed?

**Solution:**

We have,

Radius of the metallic cone, $r=12 \mathrm{~cm}$,

Height of the metallic cone, $h=24 \mathrm{~cm}$ and

Radius of the sphere, $R=2 \mathrm{~cm}$

Now,

The number of spheres so formed $=\frac{\text { Volume of the metallic cone }}{\text { Volume of a sphere }}$

$=\frac{\left(\frac{1}{3} \pi r^{2} h\right)}{\left(\frac{4}{3} \pi R^{3}\right)}$

$=\frac{r^{2} h}{4 R^{3}}$

$=\frac{12 \times 12 \times 24}{4 \times 2 \times 2 \times 2}$

$=108$

So, the number of spheres so formed is 108.