{"id":"cb_question_bank:5592dcef-6445-4439-8159-581c248a67d4","source_id":"cb_question_bank","source_item_id":"5592dcef-6445-4439-8159-581c248a67d4","external_id":"39d02567-fb2f-4a7c-a802-69186c6a894f","ibn":null,"question_id":"38517165","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.A.","skill":"Area and volume","difficulty":"M","score_band":5,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A circle has a circumference of 31 pi centimeters. What is the diameter, in centimeters, of the circle?","stimulus":"","stimulus_html":null,"stem_html":"<p>A circle has a circumference of <em><math alttext=\"31 pi\"><mrow><mn>31</mn></mrow><mi>π</mi></math></em> centimeters. What is the diameter, in centimeters, of the circle?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"31\"><mn>31</mn>\n</math>. The circumference of a circle is equal to <math alttext=\"2 pi r\"><mn>2</mn><mi>π</mi><mi>r</mi></math> centimeters, where <math alttext=\"r\"><mi>r</mi>\n</math> represents the radius, in centimeters, of the circle, and the diameter of the circle is equal to <math alttext=\"2 r\"><mrow>\n\t<mn>2</mn>\n\t<mi>r</mi>\n</mrow>\n</math> centimeters. It's given that a circle has a circumference of <math alttext=\"31 pi\"><mn>31</mn><mi>π</mi></math> centimeters. Therefore,&nbsp;<math alttext=\"31 pi equals 2 pi r\"><mn>31</mn><mi>π</mi><mo>=</mo><mn>2</mn><mi>π</mi><mi>r</mi></math>. Dividing both sides of this equation by&nbsp;<math alttext=\"pi\"><mi>π</mi></math> yields <math alttext=\"31 equals 2 r\"><mrow>\n\t<mn>31</mn>\n\t<mo>=</mo>\n\t<mrow>\n\t\t<mn>2</mn>\n\t\t<mi>r</mi>\n\t</mrow>\n</mrow>\n</math>. Since the diameter of the circle is equal to <math alttext=\"2 r\"><mrow>\n\t<mn>2</mn>\n\t<mi>r</mi>\n</mrow>\n</math> centimeters, it follows that the diameter, in centimeters, of the circle is <math alttext=\"31\"><mn>31</mn>\n</math>.</p>","correct_answer":["31"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.835000+00:00","source_updated_at":"2023-08-02T20:25:59.835000+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}}