{"kind":"task","effective_mode":"full","benchmark":{"kind":"benchmark","effective_mode":"full","slug":"math","formal_name":"MATH","introduction":"MATH organises 12,500 high-school competition problems into seven subjects and five difficulty levels, each with a full worked solution. It underlies much of the later mathematics evaluation work; this catalogue imports the full test split: 5,000 problems across all seven subjects.","introduction_ja":"","introduction_en":"","category":"Category not supplied","task_count":null,"acquisition_status":"Acquisition status not supplied","official_url":"https://github.com/hendrycks/math","indexing_mode":"index","profile":{"resources":[],"task_format":"","scoring":"","metric":"","size":"","answer_access":"","license":"","citation":"","maintainer":"","released":"","why_hard":"","related":[],"history":"","construction":"","limitations":"","saturation":"","scores":[]}},"task_id":"51672c08-28fb-5ca5-a053-e4350c63a6fa","task_key":"geometry--test--51672c08-28fb-5ca5-a053-e4350c63a6fa","task_revision_id":"1","upstream_id":"","short_description":"Polyhedron $P$ is inscribed in a sphere of radius $36$ (meaning that all…","config":"geometry","split":"test","body":"{\"level\":\"Level 5\",\"problem\":\"Polyhedron $P$ is inscribed in a sphere of radius $36$ (meaning that all vertices of $P$ lie on the sphere surface). What is the least upper bound on the ratio $$\\\\frac{\\\\text{volume of }P}{\\\\text{surface area of }P}~?$$In other words, what is the smallest real number $t$ such that $$\\\\frac{\\\\text{volume of }P}{\\\\text{surface area of }P} \\\\le t$$must be true for all polyhedra $P$ that can be inscribed in a sphere of radius $36$?\",\"type\":\"Geometry\"}","display_format":"math","language":"","answer_status":"published","assets":[],"source_url":"https://github.com/hendrycks/math","history":"initial import","indexing_mode":"index","subproblems":[],"grids":[]}