{"id":"cb_question_bank:35b5fdf9-0760-485d-9e7a-65162686bb38","source_id":"cb_question_bank","source_item_id":"35b5fdf9-0760-485d-9e7a-65162686bb38","external_id":null,"ibn":"06614-DC","question_id":"151eda3c","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 manufacturing company produces two sizes of cylindrical containers that each have a height of 50 centimeters. The radius of container A is 16 centimeters, and the radius of container B is 25% longer than the radius of container A. What is the volume, in cubic centimeters, of container B?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">A manufacturing company produces two sizes of cylindrical containers that each have a height of 50 centimeters. The radius of container A is 16 centimeters, and the radius of container B is 25% longer than the radius of container A. What is the volume, in cubic centimeters, of container B?</p>\n","rationale_html":"<p>Choice B is correct. If the radius of container A is 16 centimeters and the radius of container B is 25% longer than the radius of container A, then the radius of container B is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0877424520489e5708c92105a00b4fc3b5db98df1d649036b9481a4f5f00459b\" alt=\"16 plus, 0 point 2 5 times 16, equals 20\"></span> centimeters. The volume of a cylinder is <span class=\"italic\"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/38534e1383bebe7fa2889744c4424b1b322e38cc6d5cfd83070dc05c1e21ab18\" alt=\"pi, times r squared, times h\"></span></span>, where <span class=\"italic\">r</span> is the radius of the cylinder and <span class=\"italic\">h</span> is its height. Substituting <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ab9b4a718bf486215af2c96654fa1cc3ac986cce6f89ad06b54ecb3ce03fcfac\" alt=\"r equals 20\"></span><span class=\"italic\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/29717db47b42323b7001bd120dc44b76a1efbf6c0ea09917b9f472690199f1f2\" alt=\"h equals 50\"></span> into <span class=\"italic\"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/38534e1383bebe7fa2889744c4424b1b322e38cc6d5cfd83070dc05c1e21ab18\" alt=\"pi, times r squared, times h\"></span></span> yields that the volume of cylinder B is <span class=\"italic\"><span class=\"italic\"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ecb339a445f31487f4bf6114f863402e0d6954ae1f2a00b44401c55048c3f8d7\" alt=\"pi times open parenthesis, 20, close parenthesis, squared, times 50, equals 20,000 pi\"></span></span></span> cubic centimeters.</p><p>Choice A is incorrect and may result from multiplying the radius of cylinder B by the radius of cylinder A rather than squaring the radius of cylinder B. Choice C is incorrect and may result from multiplying the radius of cylinder B by 25 rather than squaring it. Choice D is incorrect and may result from taking the radius of cylinder B to be 25 centimeters rather than 20 centimeters.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.630000+00:00","source_updated_at":"2023-08-02T20:25:59.630000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e88f1187ca384805babceb17d01705e9bf37734b4af297dcb76dcb91dbc0c56a\" alt=\"16,000 pi\"></span></span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/503a8eeb5346cb8f5ab050e4082c9f1efdcf7c9af32bbba25fe660b0a7bbb466\" alt=\"20,000 pi\"></span></span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/af61cf829453b20c9fea36f1969a08eab1124e0779240befcb596a1c5b7e36e5\" alt=\"25,000 pi\"></span></span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/45d04a5090661c33e37301418195be06ed4dcbe6b5a2b1fe84bb94a6b76cb857\" alt=\"31,250 pi\"></span></span>\n          </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}}