AMC 10B 2003 Problem 17

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? (Note: A cone with radius r and height h has volume \pi r^{2} h / 3, and a sphere with radius r has volume 4 \pi r^{3} / 3.)

Answer Choices
A. 2: 1
B. 3: 1
C. 4: 1
D. 16: 3
E. 6: 1