A right circular cone is 8 cm high and the radius of its base is 2 cm . The cone is melted and recast into a sphere. The diameter of the sphere is

The radius of cone(r) = 2 cm ; height (h) = 8 cm;

   Volume $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times \pi \times 4\times 8=\frac{4}{3}\pi \times 2^3$

  Let radius of the sphere = r

Cone is melted and recast into sphere, so Volume of sphere = volume of cone

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

$\Rightarrow \text{diameter of sphere = 2r = 4 cm}$