An ice cream [cone](https://artofproblemsolving.com/wiki/index.php/Cone) consists of a [sphere](https://artofproblemsolving.com/wiki/index.php/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](https://artofproblemsolving.com/wiki/index.php/Radius)? 
$\mathrm{(A)}\ 2:1 \qquad\mathrm{(B)}\ 3:1 \qquad\mathrm{(C)}\ 4:1 \qquad\mathrm{(D)}\ 16:3 \qquad\mathrm{(E)}\ 6:1$
Let $r$ be the common radius of the sphere and the cone, and $h$ be the cone’s height. Then
\[75\% \cdot \left(\frac 43 \pi r^3\right) = \frac 13 \pi r^2 h \Longrightarrow h = 3r\]
Thus $h:r = 3:1$ and the answer is $\boxed{B}$.