Question 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 $\frac{\pi r^2 h}{3},$ and a sphere with radius $r$ has volume $\frac{4\pi r^3}{3}.$)