{"status": "success", "data": {"description_md": "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 cones height to its radius?\n\n$\\mathrm{(A)}\\ 2:1\\qquad\\mathrm{(B)}\\ 3:1\\qquad\\mathrm{(C)}\\ 4:1\\qquad\\mathrm{(D)}\\ 16:3\\qquad\\mathrm{(E)}\\ 6:1$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>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 <span class=\"katex--inline\">75\\%</span> of the volume of the frozen ice cream. What is the ratio of the cones height to its radius?</p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A)}\\ 2:1\\qquad\\mathrm{(B)}\\ 3:1\\qquad\\mathrm{(C)}\\ 4:1\\qquad\\mathrm{(D)}\\ 16:3\\qquad\\mathrm{(E)}\\ 6:1</span></p>&#10;<hr/>&#10;<p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2003 AMC 12B Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc12B_p14", "prev": "/problem/03_amc12B_p12"}}