{"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":"db58e55e-d474-58c6-becb-0173d46717aa","task_key":"geometry--test--db58e55e-d474-58c6-becb-0173d46717aa","task_revision_id":"1","upstream_id":"","short_description":"What is the volume of a pyramid whose base is one face of a cube of side length…","config":"geometry","split":"test","body":"{\"level\":\"Level 3\",\"problem\":\"What is the volume of a pyramid whose base is one face of a cube of side length $2$, and whose apex is the center of the cube? Give your answer in simplest form.\\n\\n[asy]\\nimport three;\\ntriple A,B,C,D,EE,F,G,H;\\nA = (0,0,0);\\nB = (1,0,0);\\nC = (1,1,0);\\nD= (0,1,0);\\nEE = (0,0,1);\\nF = B+EE;\\nG = C + EE;\\nH = D + EE;\\nO = G/2;\\ndraw(surface(B--O--C--cycle),red,nolight);\\ndraw(surface(C--O--D--cycle),red+white,nolight);\\ndraw(B--C--D);\\ndraw(B--A--D,dashed);\\ndraw(EE--F--G--H--EE);\\ndraw(A--EE,dashed);\\ndraw(B--F);\\ndraw(C--G);\\ndraw(D--H);\\ndraw(A--O--C,dashed);\\ndraw(B--O--D,dashed);\\ndot(A); dot(B); dot(C); dot(D); dot(EE); dot(F); dot(G); dot(H); dot(O);\\n[/asy]\",\"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":[]}