MathDB
Ice Cream Cone

Source:

January 4, 2009
geometry3D geometrysphereratio

Problem Statement

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% 75\% of the volume of the frozen ice cream. What is the ratio of the cone’s height to its radius? <spanclass=latexbold>(A)</span> 2:1<spanclass=latexbold>(B)</span> 3:1<spanclass=latexbold>(C)</span> 4:1<spanclass=latexbold>(D)</span> 16:3<spanclass=latexbold>(E)</span> 6:1 <span class='latex-bold'>(A)</span>\ 2: 1 \qquad <span class='latex-bold'>(B)</span>\ 3: 1 \qquad <span class='latex-bold'>(C)</span>\ 4: 1 \qquad <span class='latex-bold'>(D)</span>\ 16: 3 \qquad <span class='latex-bold'>(E)</span>\ 6: 1