{"id":"cb_practice_pdf:t5-math-m1-q23","source_id":"cb_practice_pdf","source_item_id":"t5-math-m1-q23","external_id":null,"ibn":null,"question_id":null,"program":"SAT","module":"math","domain_code":null,"domain":null,"skill_code":null,"skill":null,"difficulty":null,"score_band":null,"answer_type":"mcq","answer_source":"rationale","layout_warning":null,"form_id":"cb_practice_pdf:test-5","module_number":1,"position":23,"stem":"- -_rectangular_prism_has_a_height_of - - - -_9_inches. ~ A right The length of the prism’s base is x inches, which is 7 inches more than the width of the prism’s base. Which function V gives the volume of the prism, in cubic inches, in terms of the length of the prism’s base?","stimulus":"","stimulus_html":null,"stem_html":"<p>- -_rectangular_prism_has_a_height_of - - - -_9_inches. ~ A right The length of the prism’s base is x inches, which is 7 inches more than the width of the prism’s base. Which function V gives the volume of the prism, in cubic inches, in terms of the length of the prism’s base?</p>","rationale_html":"<p>Choice D is correct. The volume of a right rectangular prism can be represented by a function V that gives the volume of the prism, in cubic inches, in terms of the length of the prism’s base. The volume of a right rectangular prism is equal to the area of its base times its height. It’s given that the length of the prism’s base is x inches, which is 7 inches more than the width of the prism’s base. This means - that the width of the prism’s base is x 7 inches. It follows that the area of the - prism’s base, in square inches, is x^x 7h and the volume, in cubic inches, of the -7 9 prism is x^x h^ h. Thus, the function V that gives the volume of this right rectangular prism, in cubic inches, in terms of the length of the prism’s base, x, is =9 -7 V^xh x^x h. Choice A is incorrect. This function would give the volume of the prism if the height were 9 inches more than the length of its base and the width of the base were 7 inches more than its length. Choice B is incorrect. This function would give the volume of the prism if the height were 9 inches more than the length of its base. Choice C is incorrect. This function would give the volume of the prism if the width of the base were 7 inches more than its length, rather than the length of the base being 7 inches more than its width.</p>","correct_answer":["D"],"has_media":false,"has_mathml":false,"has_table":false,"source_created_at":null,"source_updated_at":null,"options":[{"label":"A","content_html":"<p>V(x) = x(x+9)(x+7) V(x) = x(x+9)(x−7)</p>","ord":0},{"label":"B","content_html":"<p>V(x) = 9x(x+7)</p>","ord":1},{"label":"C","content_html":"<p>V(x) = 9x(x−7)</p>","ord":2},{"label":"D","content_html":"","ord":3}],"attribution":{"source_id":"cb_practice_pdf","source_name":"College Board full-length SAT practice tests (PDF)","rights_holder":"College Board","canonical_url":"https://satsuite.collegeboard.org/practice/practice-tests/paper","retrieved_from":"https://satsuite.collegeboard.org/practice/practice-tests/paper","attribution":"Full-length SAT practice tests 4–11 © College Board, published free at satsuite.collegeboard.org.","disclaimer":"Extracted from PDF layout: equations, figures and tables do not survive intact. Use the original PDFs for anything the text renders poorly. SAT® is a trademark registered by the College Board, which is not affiliated with and does not endorse this project.","license":"College Board copyright. Free to download; not licensed for redistribution.","redistributable":false,"item_count":905}}