1 . 如图1所示,在梯形BCDE中,DE∥BC,且DE=
,∠C=90°,分别延长两腰交于点
,点
为线段CD上的一点,将△ADE沿DE折起到△A1DE的位置,使A1F⊥CD,如图2所示.
![](https://img.xkw.com/dksih/QBM/2022/7/7/3017582677557248/3018326812778496/STEM/36c1009f617440ed883e987f3d1b4c3c.png?resizew=344)
(1)求证:A1F⊥BE;
(2)若BC=6,AC=8,四棱锥A1-BCDE的体积为12
,求四棱锥A1-BCDE的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d452f74791f58e8400cb8d2d6038dc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/2022/7/7/3017582677557248/3018326812778496/STEM/36c1009f617440ed883e987f3d1b4c3c.png?resizew=344)
(1)求证:A1F⊥BE;
(2)若BC=6,AC=8,四棱锥A1-BCDE的体积为12
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
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2 . 已知:直四棱柱
所有棱长均为2,
.在该棱柱内放置一个球
,设球
的体积为
,直四棱柱去掉球
剩余部分的体积为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/19/6c3dd90c-c080-4177-9c8c-705f62e6d281.png?resizew=146)
(1)求三棱锥的
的表面积
;
(2)求
的最大值.(只要求写出必要的计算过程,不要求证明)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8081880e604d8f8a59f332b8167c1f17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/19/6c3dd90c-c080-4177-9c8c-705f62e6d281.png?resizew=146)
(1)求三棱锥的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac20024c3622b78dfaa2f4ef75714dee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737b04ce09bc7e1ed86dc9b3c85203b.png)
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2022-05-19更新
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913次组卷
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5卷引用:黑龙江省哈尔滨师范大学附属中学2021-2022学年高一下学期期中考试数学试题
黑龙江省哈尔滨师范大学附属中学2021-2022学年高一下学期期中考试数学试题辽宁省沈阳市第一二〇中学2021-2022学年高一6月考试数学试题(已下线)8.3.1棱柱、棱锥、棱台的表面积和体积(精讲)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)(已下线)高一数学下学期期中模拟试卷(第6章-第8章8.3)-【题型分类归纳】2022-2023学年高一数学同步讲与练(人教A版2019必修第二册)新疆乌鲁木齐市第101中学2022-2023学年高一下学期期末考试数学试题
名校
解题方法
3 . 如图,直四棱柱
的底面是边长为2的菱形,且
.
![](https://img.xkw.com/dksih/QBM/2022/6/4/2994043545329664/2997667444695040/STEM/ffc0484b-137c-43eb-8af8-7632dc71b665.png?resizew=160)
(1)证明:
.
(2)若平面
平面
.求三棱锥
的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb8fb552b9e21dbaba74d11aa747790.png)
![](https://img.xkw.com/dksih/QBM/2022/6/4/2994043545329664/2997667444695040/STEM/ffc0484b-137c-43eb-8af8-7632dc71b665.png?resizew=160)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a0e00113872f921116b6c0c3177d0f.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba0fbd88fdb064072eedd136e9cb41ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73845d4d663b3de0b281611fe2c762fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb650f48c879ea25127662b47d16feec.png)
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2022-06-09更新
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885次组卷
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3卷引用:河南省豫西部分名校2021-2022学年高一下学期月考数学试题
解题方法
4 . 如图,在三棱锥
中,E,F分别是AB,AP的中点.
![](https://img.xkw.com/dksih/QBM/2022/5/10/2976585224380416/2978040555724800/STEM/1a126ba8-051e-443a-89e4-18984488007f.png?resizew=169)
(1)求证:
平面
;
(2)若三棱锥
的各棱长均为2,求它的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://img.xkw.com/dksih/QBM/2022/5/10/2976585224380416/2978040555724800/STEM/1a126ba8-051e-443a-89e4-18984488007f.png?resizew=169)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)若三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
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2022-05-12更新
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3928次组卷
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8卷引用:新疆新和县实验中学2021-2022学年高一下学期期末考试数学试题
新疆新和县实验中学2021-2022学年高一下学期期末考试数学试题重庆市巫山县官渡中学2021-2022学年高一下学期第二次月考数学试题福建省2020-2021学年高二6月普通高中学业水平合格性考试数学试题(已下线)6.6.1柱、锥、台的侧面展开与面积(课件+练习)(已下线)模块三 专题7 大题分类练(立体几何初步)基础夯实练(人教A)(已下线)模块三 专题8(立体几何初步)基础夯实练(北师大版)(已下线)模块三 专题8 大题分类练(立体几何初步)基础夯实练(苏教版)(已下线)核心考点05简单几何体的表面积与体积-【满分全攻略】2022-2023学年高一数学下学期核心考点+重难点讲练与测试(人教A版2019必修第二册)
解题方法
5 . 如图,在三棱锥
中,
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/4/7/2953169238556672/2957121693130752/STEM/42721b43-0eb3-4219-84ea-dd90368e4140.png?resizew=178)
(1)求三棱锥
的体积和表面积
(2)若E、F分别为PA、PB的中点,求证
面EFC.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a9b8e7befcb7881c294070175b1a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5064f5ce5ac8428e277fd578da84ec6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d715e6b470395136a6c4215dbe6ff82e.png)
![](https://img.xkw.com/dksih/QBM/2022/4/7/2953169238556672/2957121693130752/STEM/42721b43-0eb3-4219-84ea-dd90368e4140.png?resizew=178)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
(2)若E、F分别为PA、PB的中点,求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2cfa68b1900da8c1a71dd832872689.png)
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2022-04-13更新
|
283次组卷
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2卷引用:浙江省台州市玉环市玉城中学2021-2022学年高一下学期第一次月考数学试题
名校
解题方法
6 . 如图,在四棱锥P﹣ABCD中,底面是矩形,且AD=2,AB=PA=1,
平面ABCD,E,F分别是线段AB,BC的中点.
;
(2)求四棱锥P﹣ABCD的表面积;
(3)求直线PE与平面PFD所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fb2fbbce7207d2b2bdd5c5ab61ecd04.png)
(2)求四棱锥P﹣ABCD的表面积;
(3)求直线PE与平面PFD所成角的大小.
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2022-11-20更新
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7卷引用:上海高二上学期期中【易错、好题、压轴60题考点专练】(2)
(已下线)上海高二上学期期中【易错、好题、压轴60题考点专练】(2)(已下线)10.3 直线与平面所成的角 (第4课时)(作业)(夯实基础+能力提升)-【教材配套课件+作业】2022-2023学年高二数学精品教学课件(沪教版2020必修第三册)上海市进才中学2021-2022学年高二上学期期中数学试题上海市华东师范大学第三附属中学2021-2022学年高二上学期12月月考数学试题上海市崇明中学2023届高三下学期第一阶段练习数学试题(已下线)第11章 简单几何体(压轴必刷30题专项训练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)(已下线)期中真题必刷压轴50题专练-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)
名校
解题方法
7 . 如图,已知四棱锥
的底面
是边长为2的正方形,
面
.
![](https://img.xkw.com/dksih/QBM/2021/11/28/2860787536486400/2861286731759616/STEM/803c6022-4309-494f-8053-bf9f535a8a93.png?resizew=273)
(1)求证:面
面
;
(2)求四棱锥
的侧面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de4c27f9ef3b9cc6899065cf4ef001e.png)
![](https://img.xkw.com/dksih/QBM/2021/11/28/2860787536486400/2861286731759616/STEM/803c6022-4309-494f-8053-bf9f535a8a93.png?resizew=273)
(1)求证:面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
20-21高一下·浙江·期末
名校
解题方法
8 . 如图,在四棱锥
中,底面
是边长为2的正方形,
,点M是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/18/1927de31-1d7f-4f5e-b589-d6565d1213d3.png?resizew=216)
(1)求证:
平面
;
(2)已知
,求三棱锥
的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65b0de5237c88a9bfffc207bab17191a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/18/1927de31-1d7f-4f5e-b589-d6565d1213d3.png?resizew=216)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30067b7b236d17af8a462f96a58d11bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135756baa58bc7e02a9df996aac9eaea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c482ee1668a59ca21f3ae8b6bad58eae.png)
您最近一年使用:0次
2022-05-02更新
|
486次组卷
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3卷引用:广东省广州市十六中2021-2022学年高一下学期期中数学试题
广东省广州市十六中2021-2022学年高一下学期期中数学试题(已下线)【新东方】高中数学20210513-005【2021】【高一下】陕西省西安市周至县第六中学2022-2023学年高一下学期5月期中数学试题
名校
9 . 如图,在四棱锥
中,
,平面
平面ABCD.
![](https://img.xkw.com/dksih/QBM/2022/5/29/2990062350671872/2991316310966272/STEM/6cf95538-0c00-4d66-927e-6dd6ee4cb87a.png?resizew=152)
(1)证明:
平面ABCD;
(2)AD与平面PBD所成角的正弦值为
,求三棱锥
的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9dd1d139678732dfc1102966c24d064.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://img.xkw.com/dksih/QBM/2022/5/29/2990062350671872/2991316310966272/STEM/6cf95538-0c00-4d66-927e-6dd6ee4cb87a.png?resizew=152)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
(2)AD与平面PBD所成角的正弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821309f088a175c00dc0f4828334503d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddfe0ccf24d760c77535a70c92dad145.png)
您最近一年使用:0次
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解题方法
10 . 如图,三棱锥
中,
,
,
两两垂直,
,
,
分别是
,
的中点,
的面积为
,四棱锥
的体积为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/18786fc0-1e66-480d-a19f-9a9d914146b6.png?resizew=170)
(1)若平面
平面
,求证:
;
(2)求三棱锥
的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75764c506b7ff847a7960ed28371f49b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/18786fc0-1e66-480d-a19f-9a9d914146b6.png?resizew=170)
(1)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd82d880985b1490bc5f4bb7fdee1cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baceb049bf16ed0fd33639fdda0ec5ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3237c82088b1ac0c5ba31b7714d5164b.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
您最近一年使用:0次
2021-10-15更新
|
2346次组卷
|
5卷引用:吉林省双辽市一中、大安市一中、通榆县一中等重点高中2021-2022学年高三上学期期末联考数学(文)试题
吉林省双辽市一中、大安市一中、通榆县一中等重点高中2021-2022学年高三上学期期末联考数学(文)试题(已下线)第03讲 空间直线、平面的平行 (精讲)-1江西省上饶市重点高中2022-2023学年高二上学期开学考试数学试题河南省联考2021-2022学年高三核心模拟卷(上)文科数学(四)(已下线)四川省成都市双流区双流棠湖中学2023-2024学年高二上学期期中数学试题