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 cone’s height to its radius? $\mathrm{(A)}\ 2:1 \qquad$ $\mathrm{(B)}\ 3:1 \qquad$ $\mathrm{(C)}\ 4:1 \qquad$ $\mathrm{(D)}\ 16:3 \qquad$ $\mathrm{(E)}\ 6:1$