{"id":"cb_question_bank:bae829cd-8d20-4d9a-9554-433ce11f45f5","source_id":"cb_question_bank","source_item_id":"bae829cd-8d20-4d9a-9554-433ce11f45f5","external_id":null,"ibn":"05721-DC","question_id":"93de3f84","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.A.","skill":"Area and volume","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The volume of right circular cylinder A is 22 cubic centimeters. What is the volume, in cubic centimeters, of a right circular cylinder with twice the radius and half the height of cylinder A?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">The volume of right circular cylinder&nbsp;A is 22&nbsp;cubic centimeters. What is the volume, in cubic centimeters, of a right circular cylinder with twice the radius and half the height of cylinder&nbsp;A?</p>\n","rationale_html":"<p>Choice C is correct. The volume of right circular cylinder A is given by the expression <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/38534e1383bebe7fa2889744c4424b1b322e38cc6d5cfd83070dc05c1e21ab18\" alt=\"pi r squared times h\"></span>, where <span class=\"italic\">r </span>is the radius of its circular base and <span class=\"italic\">h</span> is its height. The volume of a cylinder with twice the radius and half the height of cylinder A is given by <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e770a1c29239517a0d7dea6e9eea2505d85c2fab8b059d9d0f6e14813daf9b98\" alt=\"pi times, open parenthesis, 2 r, close parenthesis, squared, times one half h\"></span>, which is equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/cbb2f5066afe8b6bf1edcb925211980097dd9c2f1b2318661537b4bdc4329dbf\" alt=\"4 pi r squared, times, one half h, and equals 2 pi r squared times h\"></span>. Therefore, the volume is twice the volume of cylinder A, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ba4608b20793b8b2acaa8f96b3e5cc5c86af54a87c62bc5885ca0f1550e261e9\" alt=\"2 times 22, equals 44\"></span>.</p><p>Choice A is incorrect and likely results from not multiplying the radius of cylinder A by 2. Choice B is incorrect and likely results from not squaring the 2 in 2<span class=\"italic\">r </span>when applying the volume formula. Choice D is incorrect and likely results from a conceptual error.</p><p>&nbsp;</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.629000+00:00","source_updated_at":"2023-08-02T20:25:59.629000+00:00","options":[{"label":"A","content_html":"<p>11</p>\n","ord":0},{"label":"B","content_html":"<p>22</p>\n","ord":1},{"label":"C","content_html":"<p>44</p>\n","ord":2},{"label":"D","content_html":"<p>66</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}}