{"id":"cb_question_bank:06f8d61b-8ecf-4d83-8cb4-b0a411707558","source_id":"cb_question_bank","source_item_id":"06f8d61b-8ecf-4d83-8cb4-b0a411707558","external_id":null,"ibn":"027063-DC","question_id":"f67e4efc","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.A.","skill":"Area and volume","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A right circular cylinder has a volume of 45 pi . If the height of the cylinder is 5, what is the radius of the cylinder?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">A right circular cylinder has a volume of <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b956f082aceed7388a0e4fc9ae0b3bb3887033f973180b3cbefe59fea66ef2ef\" alt=\"45 pi\"></span></span>. If the height of the cylinder is 5, what is the radius of the cylinder?</p>\n","rationale_html":"<p>Choice A is correct. The volume of a right circular cylinder with a radius of <span class=\"italic\">r </span>is the product of the area of the base, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f4965677c6c69d7f8d902f877987923ee74d50df68cf1bc77c2d396245f47a4c\" alt=\"pi, r squared\"></span>, and the height, <span class=\"italic\">h</span>. The volume of the right circular cylinder described is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b956f082aceed7388a0e4fc9ae0b3bb3887033f973180b3cbefe59fea66ef2ef\" alt=\"45 pi\"></span> and its height is 5. If the radius is <span class=\"italic\">r</span>, it follows that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9675a3bc36499095709d66f6ee4847f5f60220a1a37d3d778660f067fcc560ff\" alt=\"45 pi equals, pi times, r, squared, times 5\"></span>. Dividing both sides of this equation by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e948b9badb1c98f562ef4a6ff4b29c6732928b862dc8a1ae59e819991a9c37c6\" alt=\"5 pi \"></span> yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c6ce84fbc6776936efc272a43e8b0d2bb8ad1e1de808c3796bf9dc328e264aa5\" alt=\"9 equals r squared\"></span>. Taking the square root of both sides yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e81b284030e0f72a6913a86f6969fd4a57667dbb414949253dee8d5b4713533f\" alt=\"r equals 3\"></span> or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9217713c160c6e589a435bd2d9428e1e58bbab7f9555a6b2a4446cbc7526568b\" alt=\"r equals negative 3\"></span>. Since <span class=\"italic\">r</span> represents the radius, the value must be positive. Therefore, the radius is 3.</p><p>Choice B is incorrect and may result from finding that the square of the radius is 9, but then from dividing 9 by 2, rather than taking the square root of 9. Choice C is incorrect. This represents the square of the radius. Choice D is incorrect and may result from solving the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9675a3bc36499095709d66f6ee4847f5f60220a1a37d3d778660f067fcc560ff\" alt=\"45 pi equals, pi times, r, squared, times 5\"></span> for <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/eb51eb71b005a4126a38b65411746fe3fa6367ce83392513168f067368c29e01\" alt=\"r squared\"></span>, not <span class=\"italic\">r</span>, by dividing by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d7ea741e12f0e85859741e2af7114e3258ad1fe9b41a83a0db21a260233b514b\" alt=\"pi\"></span> on both sides and then by subtracting, not dividing, 5 from both sides.</p><p>&nbsp;</p><p></p>\n","correct_answer":["A"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.621000+00:00","source_updated_at":"2023-08-02T20:25:59.621000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">3</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">4.5</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">9</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">40</p>\n","ord":3}],"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}}