{"id":"cb_question_bank:335873b3-d7a3-4380-9ecf-4e4373d0684e","source_id":"cb_question_bank","source_item_id":"335873b3-d7a3-4380-9ecf-4e4373d0684e","external_id":"eee80adc-71a4-4db9-8c03-1fddc462909d","ibn":null,"question_id":"c0586eb5","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":"A cylinder has a diameter of 8 inches and a height of 12 inches. What is the volume, in cubic inches, of the cylinder?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">A cylinder has a diameter of <math alttext=\"8\"><mn>8</mn>\n</math> inches and a height of <math alttext=\"12\"><mn>12</mn>\n</math> inches. What is the volume, in cubic inches, of the cylinder?</p>","rationale_html":"<p>Choice C is correct. The base of a cylinder is a circle with a diameter equal to the diameter of the cylinder. The volume, <math alttext=\"upper V\"><mi>V</mi>\n</math>, of a cylinder can be found by multiplying the area of the circular base, <math alttext=\"upper A\"><mi>A</mi>\n</math>, by the height of the cylinder, <math alttext=\"h\"><mi>h</mi>\n</math>, or <math alttext=\"upper V equals upper A h\"><mi>V</mi><mo>=</mo><mi>A</mi><mi>h</mi></math>. The area of a circle can be found using the formula <math alttext=\"upper A equals pi r squared\"><mi>A</mi><mo>=</mo><mi>π</mi><msup><mi>r</mi><mn>2</mn></msup></math>, where <math alttext=\"r\"><mi>r</mi>\n</math> is the radius of the circle. It’s given that the diameter of the cylinder is <math alttext=\"8\"><mn>8</mn>\n</math> inches. Thus, the radius of this circle is <math alttext=\"4\"><mn>4</mn>\n</math> inches. Therefore, the area of the circular base of the cylinder is <math alttext=\"upper A equals pi left parenthesis 4 right parenthesis squared\"><mi>A</mi><mo>=</mo><mi>π</mi><msup><mfenced><mn>4</mn></mfenced><mn>2</mn></msup></math>, or <math alttext=\"16 pi\"><mn>16</mn><mi>π</mi></math> square inches. It’s given that the height <math alttext=\"h\"><mi>h</mi>\n</math> of the cylinder is <math alttext=\"12\"><mn>12</mn>\n</math> inches. Substituting <math alttext=\"16 pi\"><mn>16</mn><mi>π</mi></math> for <math alttext=\"upper A\"><mi>A</mi>\n</math> and <math alttext=\"12\"><mn>12</mn>\n</math> for <math alttext=\"h\"><mi>h</mi>\n</math> in the formula <math alttext=\"upper V equals upper A h\"><mi>V</mi><mo>=</mo><mi>A</mi><mi>h</mi></math> gives <math alttext=\"upper V equals 16 pi left parenthesis 12 right parenthesis\"><mi>V</mi><mo>=</mo><mn>16</mn><mi>π</mi><mfenced><mn>12</mn></mfenced></math>, or <math alttext=\"192 pi\"><mn>192</mn><mi>π</mi></math> cubic inches.</p>\n<p>Choice A is incorrect. This is the area of the circular base of the cylinder.</p>\n<p>Choice B is incorrect and may result from using <math alttext=\"8\"><mn>8</mn>\n</math>, instead of <math alttext=\"16\"><mn>16</mn>\n</math>, as the value of <math alttext=\"r squared\"><msup><mi>r</mi><mn>2</mn></msup></math> in the formula for the area of a circle.</p>\n<p>Choice D is incorrect and may result from using <math alttext=\"8\"><mn>8</mn>\n</math>, instead of <math alttext=\"4\"><mn>4</mn>\n</math>, for the radius of the circular base.</p>","correct_answer":["C"],"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":[{"label":"A","content_html":"<p><math alttext=\"16 pi\"><mrow>\n\t<mn>16</mn>\n\t<mi>π</mi>\n</mrow>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"96 pi\"><mrow>\n\t<mn>96</mn>\n\t<mi>π</mi>\n</mrow>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"192 pi\"><mrow>\n\t<mn>192</mn>\n\t<mi>π</mi>\n</mrow>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"768 pi\"><mrow>\n\t<mn>768</mn>\n\t<mi>π</mi>\n</mrow>\n</math></p>","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}}