{"id":"cb_question_bank:c21801ca-b8b0-4c44-a207-2f0b75275ac5","source_id":"cb_question_bank","source_item_id":"c21801ca-b8b0-4c44-a207-2f0b75275ac5","external_id":null,"ibn":"070632-DC","question_id":"fb58c0db","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.D.","skill":"Circles","difficulty":"H","score_band":6,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Points A and B lie on a circle with radius 1, and arc A, B has length pi over 3 . What fraction of the circumference of the circle is the length of arc A, B ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">Points <span class=\"italic\"><span class=\"italic \">A</span></span> and <span class=\"italic\"><span class=\"italic \">B</span></span> lie on a circle with radius 1, and arc <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/870b80ebbf46a23f33cfc0f218b1314be8faa57a6d32802fb77d0e0a29c118ae\" alt=\"A, B\"></span></span> has length <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/77ae39f5189a33f18664211fb14a4a81f4c88a749296848f4d888b4c34f8a6b1\" alt=\"pi over 3\"></span></span>. What fraction of the circumference of the circle is the length of arc <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/870b80ebbf46a23f33cfc0f218b1314be8faa57a6d32802fb77d0e0a29c118ae\" alt=\"A, B\"></span></span> ?</p>\n","rationale_html":"<p>The correct answer is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b937562b5a18b41892a0bc0ac044c109853b95b8f6ec9136a2a341d8e007bf07\" alt=\"one sixth\"></span>. The circumference, <span class=\"italic\">C</span>, of a circle is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/655421265c22eaca61d0a4fa3ecd89d5cedd9ce0ba76159f4ee84eaa00a84e33\" alt=\"C equals, 2 pi, r\"></span>, where <span class=\"italic\">r</span> is the length of the radius of the circle. For the given circle with a radius of 1, the circumference is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/94576ed6df1361152657362ea94d06973edfb3c401658af330cba9f865e07093\" alt=\"C equals, 2 pi, times 1\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/48dfdcef42ecd9620103aa234a9656d7e19f423e856f8a56f8525d515cccf01f\" alt=\"C equals, 2 pi\"></span>. To find what fraction of the circumference the length of arc <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/870b80ebbf46a23f33cfc0f218b1314be8faa57a6d32802fb77d0e0a29c118ae\" alt=\"A, B\"></span> is, divide the length of the arc by the circumference, which gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4ecfd02b75b70cc8a42270053e775c59a5594067d0967c235448ee88df5d4876\" alt=\"the fraction pi over 3, end fraction, divided by 2 pi\"></span>. This division can be represented by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b7de5fa65752a8936203c536b4aa10e0080aeb752d86a82ab847c22228f3850a\" alt=\"the fraction pi over 3, end fraction, times the fraction 1 over 2 pi, end fraction, equals one sixth\"></span>. Note that 1/6, .1666, .1667, 0.166, and 0.167 are examples of ways to enter a correct answer.</p>\n","correct_answer":["1/6"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.632000+00:00","source_updated_at":"2023-08-02T20:25:59.632000+00:00","options":[],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}