{"id":"cb_question_bank:fc931a44-d56a-47ce-ab4a-3a3ec3e9dd05","source_id":"cb_question_bank","source_item_id":"fc931a44-d56a-47ce-ab4a-3a3ec3e9dd05","external_id":null,"ibn":"025459-DC","question_id":"310c87fe","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.A.","skill":"Area and volume","difficulty":"H","score_band":6,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A cube has a surface area of 54 square meters. What is the volume, in cubic meters, of the cube?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">A cube has a surface area of 54 square meters. What is the volume, in cubic meters, of the cube?</p>\n","rationale_html":"<p>Choice B is correct. The surface area of a cube with side length <span class=\"italic\">s</span> is equal to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/23ab78fb45aae7c35a99e95961d148a651e191e8f614b8519d95ec31aa01403b\" alt=\"6 s squared\"></span>. Since the surface area is given as 54 square meters, the equation <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/aabcd0f10c39d7e9f517e5f79ae12f96c2d1eddc3e5f5cd44d3143ecd7f843bc\" alt=\"54 equals, 6 s squared \"></span> can be used to solve for <span class=\"italic\">s</span>. Dividing both sides of the equation by 6 yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c926bc494bbf3bc5cb44f94d2743f303642311e0628beefd6d6d97bb765edb3f\" alt=\"9 equals, s squared\"></span>. Taking the square root of both sides of this equation yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2699499c0900dffbf5aec8036977b6a37eb83d9020b02cf63bf52976e42fa58e\" alt=\"3 equals s\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/99209628b7d84d9c542621e39914f81c224e2c314dfb7ff1f88421396a99bbb0\" alt=\"negative 3, equals s\"></span>. Since the side length of a cube must be a positive value, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6af5161d125f23c3f568658a4034063e45b4f2fcc9df75ad0bfac83412c7d757\" alt=\"s equals, negative 3 \"></span> can be discarded as a possible solution, leaving <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c2daf697bc8e8b601a931f134cf223002bd4694534ff271151118864a21de465\" alt=\"s equals 3\"></span>. The volume of a cube with side length <span class=\"italic\">s</span> is equal to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/574f9d66e566ce6216bcf270ed9fb71eca49a9211f1852f8fba4d2e2c1088a08\" alt=\"s cubed\"></span>. Therefore, the volume of this cube, in cubic meters, is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/571ef07f2ef2d3153b0c291f7a1319d57448c0a5e30e6cc556aa5fa2f8e8796c\" alt=\"3 cubed\"></span>, or 27.</p><p>Choices A, C, and D are incorrect and may result from calculation errors.</p><p>&nbsp;</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.618000+00:00","source_updated_at":"2023-08-02T20:25:59.618000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">18</p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">27</p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">36</p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">81</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}}