{"id":"aqua_rat:477b0097cb53b4093fcc2ee7c30cb7cc","source_id":"aqua_rat","source_item_id":"477b0097cb53b4093fcc2ee7c30cb7cc","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 rectangular solid, 3 x 4 x 15, is inscribed in a sphere, so that all eight of its vertices are on the sphere. What is the diameter of the sphere?","stimulus":"","stimulus_html":null,"stem_html":"<p>A rectangular solid, 3 x 4 x 15, is inscribed in a sphere, so that all eight of its vertices are on the sphere. What is the diameter of the sphere?</p>","rationale_html":"<p>In an inscribed rectangle in a sphere, we will have a line joining the opposite vertices as the diameter.</p><p>According to the Pythagoras theorem, sides 3, 4 give diagonal as 5 ==&gt; with 5 and 15, we get 5sqrt(10).</p><p>5sqrt(10) or 15.8113 is the diameter of the sphere.</p><p>answer = B</p>","correct_answer":["B"],"equiv_key":"1e06198e8eb71bcfca3ba552","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>13.3542</p>","ord":0},{"label":"B","content_html":"<p>15.8113</p>","ord":1},{"label":"C","content_html":"<p>18.3451</p>","ord":2},{"label":"D","content_html":"<p>19.5667</p>","ord":3},{"label":"E","content_html":"<p>20.8888</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":[]}