{"id":"aqua_rat:19bb0fd67ef6828eb4cf64f8af0333cc","source_id":"aqua_rat","source_item_id":"19bb0fd67ef6828eb4cf64f8af0333cc","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":"The spherical ball of lead 3 cm in diameter is melted and recast into 3 spherical balls. The diameters of two of these are 1 1/2 cm and 2 cm respectively. The diameter of third ball is?","stimulus":"","stimulus_html":null,"stem_html":"<p>The spherical ball of lead 3 cm in diameter is melted and recast into 3 spherical balls. The diameters of two of these are 1 1/2 cm and 2 cm respectively. The diameter of third ball is?</p>","rationale_html":"<p>4/3 π * 3 * 3 * 3 = 4/3 π[(3/2)3 + 23 + r3]</p><p>r = 1.25</p><p>d = 2.5</p><p>B</p>","correct_answer":["B"],"equiv_key":"b823ffd780acb154cfabb9e8","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>2.6</p>","ord":0},{"label":"B","content_html":"<p>2.5</p>","ord":1},{"label":"C","content_html":"<p>2.9</p>","ord":2},{"label":"D","content_html":"<p>3.5</p>","ord":3},{"label":"E","content_html":"<p>7.5</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":[]}