{"id":"cb_question_bank:f2569c9d-cb7a-4c5c-bc90-d091658a28c9","source_id":"cb_question_bank","source_item_id":"f2569c9d-cb7a-4c5c-bc90-d091658a28c9","external_id":null,"ibn":"070925-DC","question_id":"37dde49f","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":"The figure presents a cylindrical shape with a circular base and a larger circular top. The diameter of the circular base is labeled “k over 2,” the diameter of the circular top is labeled “k,” and the height is labeled “k.” The volume of the figure is equal to the fraction with numerator 7 pi k cubed, and denominator 48 The glass pictured above can hold a maximum volume of 473 cubic centimeters, which is approximately 16 fluid ounces. What is the value of k, in centimeters?","stimulus":"","stimulus_html":null,"stem_html":"<p><img src=\"/api/assets/2dc0806363cf7aa4ef1d848073480547554f00a34f0de980d56a264c0220ab51\" alt=\"The figure presents a cylindrical shape with a circular base and a larger circular top. The diameter of the circular base is labeled “k over 2,” the diameter of the circular top is labeled “k,” and the height is labeled “k.” The volume of the figure is equal to the fraction with numerator 7 pi k cubed, and denominator 48\" width=\"153\" height=\"119\"></p><p class=\"stem_paragraph \">The glass pictured above can hold a maximum volume of 473 cubic centimeters, which is approximately 16 fluid ounces. What is the value of <span class=\"italic\">k,</span> in centimeters?</p><p></p>\n","rationale_html":"<p>Choice D is correct. Using the volume formula <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1c942e2c2ad349cb3450c3a82c68b394dc511564cbab462b160170a1d742f52e\" alt=\"V equals, the fraction with numerator 7 pi times k cubed, and denominator 48\"></span> and the given information that the volume of the glass is 473 cubic centimeters, the value of <span class=\"italic\">k</span> can be found as follows:</p><p>\n        <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/18b5554f5cfd95bb1ec4c05294a3068523432986c8b0cfb6976d9082e90e89be\" alt=\"473 equals, the fraction with numerator 7 pi times k cubed, and denominator 48\"></span></p><p>\n        <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b35c55c4a304c31934a81d4b5fbf09055214be9afa27f03ff640b412db0c9a28\" alt=\"k cubed equals, the fraction with numerator 473 times 48, and denominator 7 pi, end fraction\"></span></p><p>\n        <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/de499804b8ff98a3400f3ad1130c65aada0c31fcb021664593d9635824772b32\" alt=\"k equals, the cube root of the fraction with numerator 473 times 48, and denominator 7 pi, end fraction, end root, which is approximately equal to 10 point 1 0 6 9 0\"></span></p><p>Therefore, the value of <span class=\"italic\">k</span> is approximately 10.11 centimeters.</p><p>Choices A, B, and C are incorrect. Substituting the values of <span class=\"italic\">k</span> from these choices in the formula results in volumes of approximately 7 cubic centimeters, 207 cubic centimeters, and 217 cubic centimeters, respectively, all of which contradict the given information that the volume of the glass is 473 cubic centimeters.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.633000+00:00","source_updated_at":"2023-08-02T20:25:59.633000+00:00","options":[{"label":"A","content_html":"<p>&nbsp; 2.52</p>\n","ord":0},{"label":"B","content_html":"<p>&nbsp; 7.67</p>\n","ord":1},{"label":"C","content_html":"<p>&nbsp; 7.79</p>\n","ord":2},{"label":"D","content_html":"<p>10.11</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}}