{"id":"cb_question_bank:9b43475c-f945-4a45-8831-bf99ef82f097","source_id":"cb_question_bank","source_item_id":"9b43475c-f945-4a45-8831-bf99ef82f097","external_id":"357b0938-dcf1-4984-934a-7d55d036717a","ibn":null,"question_id":"08b7a3f5","program":"SAT","module":"math","domain_code":"S","domain":"Geometry and Trigonometry","skill_code":"S.A.","skill":"Area and volume","difficulty":"M","score_band":5,"answer_type":"spr","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A triangular prism has a height of 8 centimeters left parenthesis cm right parenthesis and a volume of 216 cm cubed . What is the area, in cm squared , of the base of the prism? (The volume of a triangular prism is equal to upper B h , where upper B is the area of the base and h is the height of the prism.)","stimulus":"","stimulus_html":null,"stem_html":"<p>A triangular prism has a height of <math alttext=\"8 centimeters left parenthesis cm right parenthesis\"><mrow><mn>8</mn></mrow><mo>&nbsp;</mo><mtext>centimeters</mtext><mo>&nbsp;</mo><mfenced><mtext>cm</mtext></mfenced></math> and a volume of&nbsp;<math alttext=\"216 cm cubed\"><mrow><mn>216</mn></mrow><mo>&nbsp;</mo><msup><mtext>cm</mtext><mn>3</mn></msup></math>. What is the area, <math alttext=\"in cm squared\"><mtext>in</mtext><mo>&nbsp;</mo><msup><mtext>cm</mtext><mi>2</mi></msup></math>, of the base of the prism? (The volume of a triangular prism is equal to <math alttext=\"upper B h\"><mrow>\n\t<mi>B</mi>\n\t<mi>h</mi>\n</mrow>\n</math>, where <math alttext=\"upper B\"><mi>B</mi>\n</math> is the area of the base and <math alttext=\"h\"><mi>h</mi>\n</math> is the height of the prism.)</p>","rationale_html":"<p style=\"text-align: left;\">The correct answer is <math alttext=\"27\"><mn>27</mn>\n</math>. It's given that a triangular prism has a volume of <math alttext=\"216 cubic centimeters left parenthesis cm cubed right parenthesis\"><mn>216</mn><mo>&nbsp;</mo><mtext>cubic&nbsp;centimeters</mtext><mo>&nbsp;</mo><mfenced><msup><mtext>cm</mtext><mn>3</mn></msup></mfenced></math> and the volume of a triangular prism is equal to <math alttext=\"upper B h\"><mrow>\n\t<mi>B</mi>\n\t<mi>h</mi>\n</mrow>\n</math>, where <math alttext=\"upper B\"><mi>B</mi>\n</math> is the area of the base and <math alttext=\"h\"><mi>h</mi>\n</math> is the height of the prism. Therefore, <math alttext=\"216 equals upper B h\"><mn>216</mn><mo>=</mo><mi>B</mi><mi>h</mi></math>. It's also given that the triangular prism has a height of <math alttext=\"8 cm\"><mn>8</mn><mo>&nbsp;</mo><mtext>cm</mtext></math>. Therefore, <math alttext=\"h equals 8\"><mi>h</mi><mo>=</mo><mn>8</mn></math>. Substituting <math alttext=\"8\"><mn>8</mn>\n</math> for <math alttext=\"h\"><mi>h</mi>\n</math> in the equation&nbsp;<math alttext=\"216 equals upper B h\"><mn>216</mn><mo>=</mo><mi>B</mi><mi>h</mi></math> yields <math alttext=\"216 equals upper B left parenthesis 8 right parenthesis\"><mn>216</mn><mo>=</mo><mi>B</mi><mfenced><mn>8</mn></mfenced></math>. Dividing both sides of this equation by <math alttext=\"8\"><mn>8</mn>\n</math> yields <math alttext=\"27 equals upper B\"><mn>27</mn><mo>=</mo><mi>B</mi></math>. Therefore, the area, <math alttext=\"in cm squared\"><mtext>in</mtext><mo>&nbsp;</mo><msup><mtext>cm</mtext><mn>2</mn></msup></math>, of the base of the prism is <math alttext=\"27\"><mn>27</mn>\n</math>.</p>","correct_answer":["27"],"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}}