{"id":"cb_question_bank:a666adb0-1d55-48c9-bf7d-f6c7bf70c537","source_id":"cb_question_bank","source_item_id":"a666adb0-1d55-48c9-bf7d-f6c7bf70c537","external_id":null,"ibn":"05720-DC","question_id":"635f54ee","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.C.","skill":"Nonlinear functions","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The surface area of a cube is 6 times, open parenthesis, the fraction a, over 4, close parenthesis, squared , where a is a positive constant. Which of the following gives the perimeter of one face of the cube?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">The surface area of a cube is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9877c0f3a1bd6083f66cfc4cd26bc055d5e45f6565d31dff55fb4154529a192d\" alt=\"6 times, open parenthesis, the fraction a, over 4, close parenthesis, squared\"></span>, where <span class=\"italic\">a</span> is a positive constant. Which of the following gives the perimeter of one face of the&nbsp;cube?</p>\n","rationale_html":"<p>Choice B is correct. A cube has 6 faces of equal area, so if the total surface area of a cube is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9877c0f3a1bd6083f66cfc4cd26bc055d5e45f6565d31dff55fb4154529a192d\" alt=\"6 times, open parenthesis, a, over 4, close parenthesis, squared\"></span>, then the area of one face is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/af640d5655191a5e960f5ca2825ca7d405c1be1efe9ce2d5fa5a1d955b02ba60\" alt=\"open parenthesis, a, over 4, close parenthesis, squared\"></span>. Likewise, the area of one face of a cube is the square of one of its edges; therefore, if the area of one face is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/af640d5655191a5e960f5ca2825ca7d405c1be1efe9ce2d5fa5a1d955b02ba60\" alt=\"open parenthesis, a, over 4, close parenthesis, squared\"></span>, then the length of one edge of the cube is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1475809f7c833183b6b299a9a7cc8f693775c23fe816632bb97c743415abe2a0\" alt=\"a, over 4\"></span>. Since the perimeter of one face of a cube is four times the length of one edge, the perimeter is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a1e08b7112961ed7c97b2176f7ac9fdf720b4d68378b8f1c71c61ebdc06aa1a9\" alt=\"4 times the fraction a, over 4, equals a\"></span>.<br>\nChoice A is incorrect because if the perimeter of one face of the cube is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1475809f7c833183b6b299a9a7cc8f693775c23fe816632bb97c743415abe2a0\" alt=\"a, over 4\"></span>, then the total surface area of the cube is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f3bc40f4564d8996d827ffe0b0a6347bdd8c4b9ac9b9a816e996b829ae402e54\" alt=\"6 times, open parenthesis, the fraction with numerator a, over 4, and denominator 4, close parenthesis, squared, equals, 6 times, open parenthesis, a, over 16, close parenthesis, squared\"></span>, which is not <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9877c0f3a1bd6083f66cfc4cd26bc055d5e45f6565d31dff55fb4154529a192d\" alt=\"6 times, open parenthesis, a, over 4, close parenthesis, squared\"></span>. Choice C is incorrect because if the perimeter of one face of the cube is 4<span class=\"italic\">a</span>, then the total surface area of the cube is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0b08e1df32b498a4a3af7fdb959f42386bc22ddfc99129990649448a9d984450\" alt=\"6 times, open parenthesis, the fraction 4 a, over 4, close parenthesis, squared, equals 6 a, squared\"></span>, which is not <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9877c0f3a1bd6083f66cfc4cd26bc055d5e45f6565d31dff55fb4154529a192d\" alt=\"6 times, open parenthesis, a, over 4, close parenthesis, squared\"></span>. Choice D is incorrect because if the perimeter of one face of the cube is 6<span class=\"italic\">a</span>, then the total surface area of the cube is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c76a7629578e55d856a9a02305984ea5e2a95eadc774729ffa27a6b646f2a053\" alt=\"6 times, open parenthesis, the fraction 6 a, over 4, close parenthesis, squared, equals, 6 times, open parenthesis, the fraction 3 a, over 2, close parenthesis, squared\"></span>, which is not <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9877c0f3a1bd6083f66cfc4cd26bc055d5e45f6565d31dff55fb4154529a192d\" alt=\"6 times, open parenthesis, a, over 4, close parenthesis, squared\"></span>.</p>\n","correct_answer":["B"],"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":"<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1475809f7c833183b6b299a9a7cc8f693775c23fe816632bb97c743415abe2a0\" alt=\"the fraction a, over 4\"></span>\n","ord":0},{"label":"B","content_html":"<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/312ccc3f341afef6fd0d63cb9a21f50d9a0ff66b6f3d8c37bb09f474aae7d490\" alt=\"a\"></span>\n","ord":1},{"label":"C","content_html":"<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8229194124d3c2906cc08406962bb3c207260f83b1ce596b86a550841eee9361\" alt=\"4 a\"></span>\n","ord":2},{"label":"D","content_html":"<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a295fe872465a2c5cbd8528d7f4eef054c67ec8e2cffcb877af1926e87db3d5d\" alt=\"6 a\"></span>\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}}