2003 AMC 12B Problem 13

An ice cream cone consists of a sphere of vanilla ice cream and a right circular cone that has the same diameter as the sphere. If the ice cream melts, it will exactly fill the cone. Assume that the melted ice cream occupies $75\%$ of the volume of the frozen ice cream. What is the ratio of the cones height to its radius?

$\mathrm{(A)}\ 2:1\qquad\mathrm{(B)}\ 3:1\qquad\mathrm{(C)}\ 4:1\qquad\mathrm{(D)}\ 16:3\qquad\mathrm{(E)}\ 6:1$

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.