{"id":"cb_question_bank:67cfc8a7-76f7-4383-b803-7aa9fe064a1d","source_id":"cb_question_bank","source_item_id":"67cfc8a7-76f7-4383-b803-7aa9fe064a1d","external_id":"933baf7b-cfc3-42f9-a9f8-f184d6f97c27","ibn":null,"question_id":"7d721177","program":"SAT","module":"math","domain_code":"Q","domain":"Problem-Solving and Data Analysis","skill_code":"Q.A.","skill":"Ratios, rates, proportional relationships, and units","difficulty":"H","score_band":7,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The density of a certain type of wood is 353 kilograms per cubic meter. A sample of this type of wood is in the shape of a cube and has a mass of 345 kilograms. To the nearest hundredth of a meter , what is the length of one edge of this sample?","stimulus":"","stimulus_html":null,"stem_html":"

The density of a certain type of wood is 353\n kilograms per cubic meter. A sample of this type of wood is in the shape of a cube and has a mass of 345\n kilograms. To the nearest hundredth of a meter, what is the length of one edge of this sample? 

","rationale_html":"

Choice B is correct. It’s given that the density of a certain type of wood is 353\n kilograms per cubic meter kg/m3, and a sample of this type of wood has a mass of 345 kg. Let x\n represent the volume, in m3, of the sample. It follows that the relationship between the density, mass, and volume of this sample can be written
as 353 kg1 m3=345 kgx m3, or 353=345x. Multiplying both sides of this equation by x\n yields 353x=345. Dividing both sides of this equation by 353\n yields x=345353. Therefore, the volume of this sample is 345353 m3. Since it’s given that the sample of this type of wood is a cube, it follows that the length of one edge of this sample can be found using the volume formula for a cube, V=s3, where V\n represents the volume, in m3, and s\n represents the length, in m, of one edge of the cube. Substituting 345353for V\n in this formula yields 345353=s3. Taking the cube root of both sides of this equation yields 3453533=s, or s≈0.99. Therefore, the length of one edge of this sample to the nearest hundredth of a meter is 0.99\n.

\n

Choices A, C, and D are incorrect and may result from conceptual or calculation errors.

","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.829000+00:00","source_updated_at":"2023-08-02T20:25:59.829000+00:00","options":[{"label":"A","content_html":"

0.98\n

","ord":0},{"label":"B","content_html":"

0.99\n

","ord":1},{"label":"C","content_html":"

1.01\n

","ord":2},{"label":"D","content_html":"

1.02\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}}