{"id":"aqua_rat:4408d544854e19f28bea49ffd1c81bac","source_id":"aqua_rat","source_item_id":"4408d544854e19f28bea49ffd1c81bac","external_id":null,"program":null,"section":"math","category_code":"PHM","category":"Preparing for Higher Math","subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":null,"scored":true,"layout_warning":null,"stem":"A hollow cube of size 5cm is taken, with the thickness of 1cm. It is made of smaller cubes of size 1cm .If the outer surface of the cube is painted how many faces of the smaller cubes remain unpainted?","stimulus":"","stimulus_html":null,"stem_html":"<p>A hollow cube of size 5cm is taken, with the thickness of 1cm. It is made of smaller cubes of size 1cm .If the outer surface of the cube is painted how many faces of the smaller cubes remain unpainted?</p>","rationale_html":"<p>Volume of Big Cube considering it is not hollow = L3 = 5*5*5 = 125 cm3</p><p>Size of hollow cube (considering 1 cm thickness on two faces of large cube = 5 - 2 = 3cm</p><p>Volume of hollow cube = 3*3*3 = 27 cm3</p><p>So Total Volume filled up by smaller cubes = Volume of Larger Cube - Volume of hollow cube</p><p>= 125 - 27</p><p>= 98 cm3</p><p>Volume of 1 small cube = 1*1*1 = 1 cm3</p><p>Total number of small cubes in the larger cube = 98 / 1 = 98</p><p>and Number of faces of 98 small cubes (6 faces each cube has) = 98*6 = 588 faces</p><p>Total Surface area of 6 faces of larger cube painted = 6*L2 = 6*5*5 = 150cm2</p><p>Surface area of one face of small cube = 1*1 = 1cm2</p><p>Number of faces of small cube painted = 150/1 = 150 faces</p><p>Hence number of faces of the smaller cubes remain unpainted= 588-150</p><p>= 438</p><p>answer.A</p>","correct_answer":["A"],"equiv_key":"8ff8a8babec619edc72a6dcf","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>438</p>","ord":0},{"label":"B","content_html":"<p>550</p>","ord":1},{"label":"C","content_html":"<p>500</p>","ord":2},{"label":"D","content_html":"<p>450</p>","ord":3},{"label":"E","content_html":"<p>498</p>","ord":4}],"passage":null,"attribution":{"source_id":"aqua_rat","source_name":"AQuA-RAT algebra word problems with rationales","rights_holder":"Google DeepMind and the AQuA-RAT contributors","canonical_url":"https://github.com/google-deepmind/AQuA","retrieved_from":"https://raw.githubusercontent.com/google-deepmind/AQuA/master/","attribution":"Algebra word problems from the AQuA-RAT dataset (Ling et al., 2017), published by Google DeepMind under the Apache License 2.0.","disclaimer":"AQuA-RAT items are crowdsourced algebra problems, not ACT questions. They carry five answer choices in the pre-2025 ACT Mathematics style and no ACT reporting category. Useful for drilling Preparing for Higher Math content; not a substitute for a real form.","license":"Apache License 2.0. Crowdsourced by DeepMind and published for free use, including commercially.","redistributable":true,"item_count":508},"equivalents":[]}