{"id":"aqua_rat:40b265616499bd97fe1937dfd1fa8050","source_id":"aqua_rat","source_item_id":"40b265616499bd97fe1937dfd1fa8050","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 sphere is surrounded by the smallest cylinder that will just contain it. Which of following is a complete set of the points where the cylinder touches the sphere? I. One point, II. Two points, III. A Circle","stimulus":"","stimulus_html":null,"stem_html":"<p>A sphere is surrounded by the smallest cylinder that will just contain it. Which of following is a complete set of the points where the cylinder touches the sphere?</p><p>I. One point,</p><p>II. Two points,</p><p>III. A Circle</p>","rationale_html":"<p>Explanations</p><p>(1) Let’s use the familiar reference points of Earth’s geography to talk about the sphere. The cylinder fits the sphere tightly, so it touches the sphere around its “equator.” The top of the cylinder touches the “north pole” of the sphere, and the bottom of the cylinder symmetrically touches the “south pole” of the sphere. That’s a circle (the equator) and two points (the north &amp; south poles). Answer E.</p>","correct_answer":["E"],"equiv_key":"7221ede7ee61e57551585c39","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>I only</p>","ord":0},{"label":"B","content_html":"<p>II only</p>","ord":1},{"label":"C","content_html":"<p>III only</p>","ord":2},{"label":"D","content_html":"<p>I &amp; III</p>","ord":3},{"label":"E","content_html":"<p>II &amp; III</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":[]}