Question

If a sphere of radius r is melted and recast into a cone of height h what will be the radius of the base of the cone

Answer 1

volume remains same when the sphere is melted and recast into the cone.

volume of sphere = $\frac{4}{3}\pi r^3$

base radius of cone = R.    Volume of cone = $\frac{1}{3}\pi R^2 h$

equating them:  $R^2=\frac{4r^3}{h}\ \ \implies\ \ R=2*\sqrt{\frac{r^3}{h}}$