{"id":"cb_question_bank:4785f6f3-cb7a-4e93-a8ef-f8f2082d46e1","source_id":"cb_question_bank","source_item_id":"4785f6f3-cb7a-4e93-a8ef-f8f2082d46e1","external_id":"31c28a2a-1001-4c2c-b27f-aa2b2380c77d","ibn":null,"question_id":"ba8ca563","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":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A cube has a volume of 474,552 cubic units. What is the surface area, in square units, of the cube?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">A cube has a volume of <math alttext=\"474,552\"><mn>474,552</mn>\n</math> cubic units. What is the surface area, in square units, of the cube?</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"36,504\"><mn>36,504</mn>\n</math>. The volume of a cube can be found using the formula <math alttext=\"upper V equals s cubed\"><mrow>\n\t<mi>V</mi>\n\t<mo>=</mo>\n\t<msup>\n\t\t<mi>s</mi>\n\t\t<mn>3</mn>\n\t</msup>\n</mrow>\n</math>, where <math alttext=\"s\"><mi>s</mi>\n</math> represents the edge length of a cube. It’s given that this cube has a volume of <math alttext=\"474,552\"><mn>474,552</mn>\n</math> cubic units. Substituting <math alttext=\"474,552\"><mn>474,552</mn>\n</math> for <math alttext=\"upper V\"><mi>V</mi>\n</math> in <math alttext=\"upper V equals s cubed\"><mi>V</mi><mo>=</mo><msup><mi>s</mi><mn>3</mn></msup></math> yields <math alttext=\"474,552 equals s cubed\"><mrow>\n\t<mn>474,552</mn>\n\t<mo>=</mo>\n\t<msup>\n\t\t<mi>s</mi>\n\t\t<mn>3</mn>\n\t</msup>\n</mrow>\n</math>. Taking the cube root of both sides of this equation yields <math alttext=\"78 equals s\"><mn>78</mn><mo>=</mo><mi>s</mi></math>. Thus, the edge length of the cube is <math alttext=\"78\"><mn>78</mn>\n</math> units. Since each face of a cube is a square, it follows that each face has an edge length of <math alttext=\"78\"><mn>78</mn>\n</math> units. The area of a square can be found using the formula <math alttext=\"upper A equals s squared\"><mrow>\n\t<mi>A</mi>\n\t<mo>=</mo>\n\t<msup>\n\t\t<mi>s</mi>\n\t\t<mn>2</mn>\n\t</msup>\n</mrow>\n</math>. Substituting <math alttext=\"78\"><mn>78</mn>\n</math> for <math alttext=\"s\"><mi>s</mi>\n</math> in this formula yields <math alttext=\"upper A equals 78 squared\"><mi>A</mi><mo>=</mo><msup><mn>78</mn><mn>2</mn></msup></math>, or <math alttext=\"upper A equals 6,084\"><mrow>\n\t<mi>A</mi>\n\t<mo>=</mo>\n\t<mn>6,084</mn>\n</mrow>\n</math>. Therefore, the area of one face of this cube is <math alttext=\"6,084\"><mn>6,084</mn>\n</math> square units. Since a cube has <math alttext=\"6\"><mn>6</mn>\n</math> faces, the surface area, in square units, of this cube is <math alttext=\"6 left parenthesis 6,084 right parenthesis\"><mn>6</mn><mfenced><mn>6,084</mn></mfenced></math>, or <math alttext=\"36,504\"><mn>36,504</mn>\n</math>.</p>","correct_answer":["36504"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.836000+00:00","source_updated_at":"2023-08-02T20:25:59.836000+00:00","options":[],"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}}