{"id":"cb_question_bank:eb401d7c-45d1-4e17-b436-476997129429","source_id":"cb_question_bank","source_item_id":"eb401d7c-45d1-4e17-b436-476997129429","external_id":null,"ibn":"00113-DC","question_id":"a2e76b60","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":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"A cylindrical can containing pieces of fruit is filled to the top with syrup before being sealed. The base of the can has an area of 75 centimeters squared , and the height of the can is 10 cm. If 110 centimeters cubed of syrup is needed to fill the can to the top, which of the following is closest to the total volume of the pieces of fruit in the can?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">A cylindrical can containing pieces of fruit is filled to the top with syrup before being sealed. The base of the can has an area of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/03c232ab0a438883c04a9ddea4de9a81d50b36831bcc8e96efee553764c1f77e\" alt=\"75 centimeters squared\"></span><sup><span class=\"math_expression \"></span></sup>, and the height of the can is 10 cm. If <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9e5b9a1db2d1128b4a36cdbcbd857686c676c5168a624d849c63fcac645950fb\" alt=\"110 centimeters cubed\"></span><sup><span class=\"math_expression \"></span></sup> of syrup is needed to fill the can to the top, which of the following is closest to the total volume of the pieces of fruit in the can?</p>\n","rationale_html":"<p>Choice C is correct. The total volume of the cylindrical can is found by multiplying the area of the base of the can, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/03c232ab0a438883c04a9ddea4de9a81d50b36831bcc8e96efee553764c1f77e\" alt=\"75 square centimeters\"></span>, by the height of the can, 10 cm, which yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/41d80f1889fdfa9b831d73e06f3aca12a13fc5b4dcf6d2c98d0cc2aeb3e62f0f\" alt=\"750 cubic centimeters\"></span>. If the syrup needed to fill the can has a volume of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9e5b9a1db2d1128b4a36cdbcbd857686c676c5168a624d849c63fcac645950fb\" alt=\"110 cubic centimeters\"></span>, then the remaining volume for the pieces of<br>\nfruit is <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/91f7a91a3311ea199fd96535d8d9a9490a63da39c23acaba9988a0bf1a4640a2\" alt=\"750 minus 110, equals 640 cubic centimeters\"></span>.</p><p>Choice A is incorrect because if the fruit had a volume of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8e7c9df6ea0f3190a0fbf2f2f6149ad420240648e618935bfb3aed9e4f8124cb\" alt=\"7 point 5 cubic centimeters\"></span>, there would be <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/2c83ea5bd67288b5cb634d38bf858c9bba9aea285d361eeffa04888316e7eaf9\" alt=\"750 minus 7 point 5, equals 742 point 5 cubic centimeters\"></span> of syrup needed to fill the can to the top. Choice B is incorrect because if the fruit had a volume of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3474f1e544387e9b339007b124dfeaf5588d64b771c9c667daf0b554895b43bf\" alt=\"185 cubic centimeters\"></span>, there would be <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/de638f0ba67ff00908950f2c6afa8942bffe01cfa50c210dfcf0d039632b8950\" alt=\"750 minus 185, equals 565 cubic centimeters\"></span> of syrup needed to fill the can to the top. Choice D is incorrect because it is the total volume of the can, not just of the pieces of fruit.</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.614000+00:00","source_updated_at":"2023-08-02T20:25:59.614000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \"></span>\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8e7c9df6ea0f3190a0fbf2f2f6149ad420240648e618935bfb3aed9e4f8124cb\" alt=\"7 point 5 centimeters cubed\"></span></p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \"></span>\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3474f1e544387e9b339007b124dfeaf5588d64b771c9c667daf0b554895b43bf\" alt=\"185 centimeters cubed\"></span></p>\n","ord":1},{"label":"C","content_html":"<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a4be79be4ed348dc50303f6338ac2f22fdebbe5de6d3060df4981f1857f242f1\" alt=\"640 centimeters cubed\"></span>\n","ord":2},{"label":"D","content_html":"<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/41d80f1889fdfa9b831d73e06f3aca12a13fc5b4dcf6d2c98d0cc2aeb3e62f0f\" alt=\"750 centimeters cubed\"></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}}