1 . 已知圆锥的母线长度为3,一只蚂蚁从圆锥的底面圆上一点出发,绕着圆锥侧面爬行一周,再回到出发点的最短距离为3,则此圆锥的底面圆半径为____________ .
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解题方法
2 . 如图,在棱长为2的正方体
中,E,F分别是
,
的中点.
![](https://img.xkw.com/dksih/QBM/2022/1/5/2847429027332096/2892419725180928/STEM/5f7e9ffa-7453-4667-8bd7-c723c2979427.png?resizew=174)
(1)求点
到平面
的距离;
(2)若G是棱
上一点,当
平面
时,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://img.xkw.com/dksih/QBM/2022/1/5/2847429027332096/2892419725180928/STEM/5f7e9ffa-7453-4667-8bd7-c723c2979427.png?resizew=174)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
(2)若G是棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f100f1e48d34169f4f90aad15d02e67c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
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2022-01-11更新
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986次组卷
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9卷引用:湖北省鄂东南三校联考2021-2022学年高二上学期阶段考试(一)数学试题
湖北省鄂东南三校联考2021-2022学年高二上学期阶段考试(一)数学试题广西贺州市昭平县昭平中学2021-2022学年高二上学期第一次月考数学(理)试题湖北省武汉市第十九中学2023-2024学年高二上学期10月月考数学试题重庆市万州清泉中学2022-2023学年高二上学期9月月考数学试题广东省珠海市第二中学2022-2023学年高二上学期10月月考数学试题福建省漳州市第三中学2022-2023学年高二下学期期中数学试题陕西省部分学校(神木中学等学校)2023-2024学年高二上学期10月月考数学试题广东省广州市真光中学2023-2024学年高二上学期9月阶段性质量检测数学试题(已下线)模块一 专题2 A 空间向量的应用基础卷 期末终极研习室高二人教A版
名校
3 . 如图,在三棱柱
中,点E,F分别在棱
,
上(均异于端点),
,
,
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/5e3a0c86-a33d-40dd-8b75-8cd8c5393f2c.png?resizew=260)
(1)求证:四边形
是矩形;
(2)若
,
,求平面
与平面
所成锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbec5434bcf9173dfeebd92aa0c5070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dba9cf66066aafbafb6116928eeb10ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d25e8fc3dda4f8b45491514b6e22a962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/5e3a0c86-a33d-40dd-8b75-8cd8c5393f2c.png?resizew=260)
(1)求证:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6480f384476190883f06c0289c7519.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c4599c8c996873814673237b8942df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d9e036eecc9aebcc2d2a2855bbfafdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
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2021-09-18更新
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1741次组卷
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4卷引用:湖北省新高考九师联盟2021届高三下学期2月质检巩固数学试题
湖北省新高考九师联盟2021届高三下学期2月质检巩固数学试题黑龙江省哈尔滨市第三中学2021-2022学年高二上学期10月月考数学试题(已下线)专题04 二面角(含探索性问题)-【解题思路培养】2022年高考数学一轮复习解答题拿分秘籍(全国通用版)四川省内江市第六中学2022届高三下学期考前强化训练二数学(理科)试题
名校
4 . 如图所示,在球
的内接八面体
中,顶点
,
分别在平面
两侧,且四棱锥
与
都是正四棱锥.设二面角
的平面角的大小为
,则
的取值可能为( ).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/ac4f34b2-80de-4098-a525-a64d496111e9.png?resizew=160)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73cbd9eb22f75ad5304d8491b314a9a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c6caa0455442437177ab9b995df37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f96627abd793ca157d4dd1587f584d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/ac4f34b2-80de-4098-a525-a64d496111e9.png?resizew=160)
A.![]() | B.3 | C.![]() | D.1 |
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5 . 如图,正三棱锥
中,
,侧棱长为
,过点
的平面与侧棱
相交于
,则△
的周长的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0556ae9095d60cad5cd7b2f455ec81a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df7fc746f8c4801d8f2f0471ba3297e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf237230e88f82ad330b73dbc24a0de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86eec8526479272d15bb3b171a46de0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2021-08-06更新
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1084次组卷
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10卷引用:湖北省黄冈市2020-2021学年高一下学期期末数学试题
湖北省黄冈市2020-2021学年高一下学期期末数学试题广东省肇庆中学2021-2022学年高二上学期开学考试数学试卷(已下线)第九章 立体几何专练4—简单几何体的表面积与体积2-2022届高三数学一轮复习(已下线)8.1 基本立体图形(精练)-2021-2022学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)8.1 基本立体图形(已下线)期中测试·B卷-【重难点突破】2021-2022学年高一数学常考题专练(人教A版2019必修第二册)(已下线)第19讲 空间几何体概念(已下线)专题8.2 基本立体图形(重难点题型检测)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)(已下线)核心考点6 立体几何中组合体 B提升卷 (高一期末考试必考的10大核心考点) (已下线)专题07 立体几何表面积、体积、截面和点线面的8种常考题型归类(1) -《期末真题分类汇编》(北师大版(2019))
名校
6 . 如图1,在平行四边形
中,
=60°,
,
,
,
分别为
,
的中点,现把平行四边形
沿
折起如图2所示,连接
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/b8e39710-99eb-4ef5-abe1-9a672673aa4c.png?resizew=396)
(1)求证:
;
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883732ae71bfed76e07732ec709f4653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b5d693c4f0c4d0e6c0c810e7d464b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883732ae71bfed76e07732ec709f4653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa6cb992b6faad4744f85d73a3b76dd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a56f2e56229a722d1f40d74d3967a3d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/b8e39710-99eb-4ef5-abe1-9a672673aa4c.png?resizew=396)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82c2b3adb41e8965f553da2e5086a751.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a677b42f8b427b21924a559b90141d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c44507c93f6180afd1697d2fa5a5c741.png)
您最近一年使用:0次
2021-06-15更新
|
1645次组卷
|
12卷引用:湖北省武汉一中2021届高三下学期二模数学试题
湖北省武汉一中2021届高三下学期二模数学试题广东省广州市广州大学附属中学2021-2022学年高二上学期第一次月考数学试题广东省真光中学2021-2022学年高二上学期10月月考数学试题2016届福建福州市高三上学期期末数学(理)试卷2017届河南南阳一中高三理上学期月考四数学试卷宁夏石嘴山市第三中学2017届高三下学期第三次模拟考试数学(理)试题河南省南阳市2018届高三期终质量评估数学(理)试题广西南宁二中2020届高三4月开学考试理数试题四川省成都市实验外国语学校2020届高三(高2017级)数学模拟(三)理试题(已下线)专题19 立体几何综合-2020年高考数学(理)母题题源解密(全国Ⅲ专版)(已下线)2022年高考考前20天终极冲刺攻略(三)【理科数学】 (5月27日)2023版 北师大版(2019) 选修第一册 突围者 第三章 专项拓展训练3 用空间向量解决折叠问题
7 . 如图,在三棱锥
中,
,
,
,
,直线
与平面
所成角为
,
在
上且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/cbbe3b87-562c-43ca-8cb0-240b796e4d9f.png?resizew=170)
(1)若
,求证:平面
平面
;
(2)若
,求直线
与平面
所成角的正弦值的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4fde24e68a4db5d618e608082b0781e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b96fac11d72f72c805dbddb8da72d68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dee6c1410e79934b560642684807e70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ba7a4f5ec17e1792c9a7ed23349bbbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb6bf23a5a12e1ba5413594d7b1a57c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/3/cbbe3b87-562c-43ca-8cb0-240b796e4d9f.png?resizew=170)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bbd432d8e24ffec6bd5782d0e9dcb1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c9909a043e0fc127af97617b67576eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
名校
解题方法
8 . 如图所示,在四棱锥
中,侧面
底面
,侧棱
,
,底面
为直角梯形,其中
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2020/11/5/2586476835667968/2601100372549632/STEM/32345b8b55bf47e4b1786b3cbad37ae8.png?resizew=152)
(1)求直线
与平面
所成角的余弦值;
(2)求
点到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1328e05d150f86dbe18656662eaa8f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0453cfd7e92bf7746a88280b9e7b580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5acb763021bf166ca719d07223591d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/2020/11/5/2586476835667968/2601100372549632/STEM/32345b8b55bf47e4b1786b3cbad37ae8.png?resizew=152)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30f457418e6a7e21f0ed0bf490a3709c.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2020-11-26更新
|
1805次组卷
|
5卷引用:湖北省荆州市沙市中学2020-2021学年高二上学期期末数学试题
9 . 过
所在平面
外一点
,作
,垂足为
,连接
,
,
,则下列结论错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59169f91ebc758ba6e73fc99fcfaab15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
A.若![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() |
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解题方法
10 . 在四棱锥
中,
⊥底面
,
,
,则四棱锥的外接球的表面积为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead32f6e1869038b83dd9dffb0912515.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fedc3e5ada94e1764f198f1853aaf64.png)
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2020-08-03更新
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