{"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 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 $4 \\pi r^3 / 3$.)\n\n$\\textbf{(A) } 2:1 \\qquad\\textbf{(B) } 3:1 \\qquad\\textbf{(C) } 4:1 \\qquad\\textbf{(D) } 16:3 \\qquad\\textbf{(E) } 6:1$", "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 cone&#8217;s height to its radius? (Note: a cone with radius  <span class=\"katex--inline\">r</span>  and height  <span class=\"katex--inline\">h</span>  has volume  <span class=\"katex--inline\">\\pi r^2 h / 3</span>  and a sphere with radius  <span class=\"katex--inline\">r</span>  has volume  <span class=\"katex--inline\">4 \\pi r^3 / 3</span> .)</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } 2:1 \\qquad\\textbf{(B) } 3:1 \\qquad\\textbf{(C) } 4:1 \\qquad\\textbf{(D) } 16:3 \\qquad\\textbf{(E) } 6:1</span> </p>\n<hr><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>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2003 AMC 10B Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/03_amc10B_p18", "prev": "/problem/03_amc10B_p16"}}