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收录高三寒假作业44新题

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wangweiye7840 2024-01-25 12:32:12 +08:00
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工具v2/文本文件/新题收录列表.txt
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@ -130,3 +130,6 @@
20240125-122954
004230,023950:023953,011258
20240125-123201
023954:023956,016816,023957:023959

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题库0.3/Problems.json
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@ -645744,6 +645744,126 @@
"space": "",
"unrelated": []
},
"023954": {
"id": "023954",
"content": "已知球的表面积为 $64 \\pi \\mathrm{cm}^2$, 若用一个平面截球, 使截面圆的半径为 $2 \\mathrm{cm}$, 则截面与球心的距离是\\blank{50} $\\mathrm{cm}$.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240125\t毛培菁"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"023955": {
"id": "023955",
"content": "若棱长为 $2$ 的正方体的八个顶点在同一球面上, 则此球的表面积为\\blank{50}.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240125\t毛培菁"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"023956": {
"id": "023956",
"content": "若三球的半径之比是 $1: 2: 3$, 则半径最大的球体积是其余两球体积和的倍.",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240125\t毛培菁"
],
"same": [],
"related": [],
"remark": "",
"space": "4em",
"unrelated": []
},
"023957": {
"id": "023957",
"content": "把一个表面积为 $16 \\pi \\mathrm{cm}^2$ 的实心铁球铸成一个底面半径与球的半径一样的圆锥, 若没有任何损耗, 则圆锥的高是\\blank{50}$\\mathrm{cm}$.",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240125\t毛培菁"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"023958": {
"id": "023958",
"content": "右图是一个装有水的倒圆锥形杯子, 杯子口径 $6 \\mathrm{cm}$, 高 $8 \\mathrm{cm}$ (不含杯脚), 已知水的高度是 $4 \\mathrm{cm}$, 现往杯子中放入一种直径为 $1 \\mathrm{cm}$ 的珍珠, 该珍珠放入水中后直接沉入杯底, 且体积不变. 若放完珍珠后水不溢出, 则最多可以放入珍珠\\blank{50}颗.\n\\begin{center}\n\\begin{tikzpicture}[>=latex, scale = 0.3]\n\\draw (0,0) coordinate (O);\n\\draw (-3,8) coordinate (A);\n\\draw (3,8) coordinate (B);\n\\draw (A)--(O)--(B);\n\\draw ($(O)!0.5!(A)$) coordinate (P);\n\\draw (P) arc (180:540:1.5 and {1.5/4});\n\\draw (A) arc (180:540:3 and 0.75);\n\\filldraw (O)--++ (0.1,-0.1) --++ (0,-1.9) --++ (-0.2,0) --++ (0,1.9) -- cycle;\n\\filldraw (0,-2) ellipse (1.5 and {1.5/4});\n\\end{tikzpicture}\n\\end{center}",
"objs": [],
"tags": [],
"genre": "填空题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240125\t毛培菁"
],
"same": [],
"related": [],
"remark": "",
"space": "",
"unrelated": []
},
"023959": {
"id": "023959",
"content": "已知球的半径为 $R$, 在球内作一个内接圆柱, 这个圆柱底面半径与高为何值时, 它的侧面积最大? 侧面积的最大值是多少?",
"objs": [],
"tags": [],
"genre": "解答题",
"ans": "",
"solution": "",
"duration": -1,
"usages": [],
"origin": "自拟题目",
"edit": [
"20240125\t毛培菁"
],
"same": [],
"related": [],
"remark": "",
"space": "4em",
"unrelated": []
},
"030001": {
"id": "030001",
"content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",