Two solid right cones of equal height and of radii r₁ and r₂ are melted and made to form a solid sphere of radius R. Then the height of the cone is

$$\eqalign{ & {\text{Let the height be }}H \cr & \Rightarrow \frac{1}{3}\pi r_1^2H + \frac{1}{3}\pi r_2^2H = \frac{4}{3}\pi {R^3} \cr & \Rightarrow \frac{1}{3}\pi H\left( {r_1^2 + r_2^2} \right) = \frac{4}{3}\pi {R^3} \cr & \Rightarrow H = \frac{{4{R^3}}}{{r_1^2 + r_2^2}} \cr} $$