Difficult# Volume of a Snowcone

SATMAT-KJYLC0

A snowcone consists of a spherical flavored ball of ice set in a paper right circular cone. The spherical ball of ice and the circular base of the cone have identical diameters, and the depth of the cone is two times the length of the diameter.

If all of the ice melts, then what percent of the paper cone will be filled?

Assume that the melted ice occupies the same amount of space as the frozen ice.