1 . 已知
是边长为
正三角形
的外心,沿
将该三角形折成直二面角
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de908dd52536dc51de6e71920c847d9.png)
A.直线![]() ![]() |
B.直线![]() ![]() ![]() |
C.平面![]() ![]() ![]() |
D.![]() ![]() ![]() |
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解题方法
2 . 已知正方体
的所有顶点均在体积为
的球O上,则该正方体的棱长为___________ ,若动点P在四边形
内运动,且满足直线
与直线
所成角的正弦值为
,则
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bea86620b6ce1284536813e1a74837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f645d4b09fba53f971172cd2602c691.png)
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3 . 如图,AB为圆锥SO底面圆O的直径,点C是圆O上异于A,B的一点,N为SA的中点,则圆O上存在点M使( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/1969d76b-2b23-4b8d-9737-4fba06fe4513.png?resizew=167)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/1969d76b-2b23-4b8d-9737-4fba06fe4513.png?resizew=167)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4 . 如图,棱长为2的正方体
中,P为线段
上动点(包括端点).则以下结论正确的为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/a5efef69-8452-47f8-9267-86c994b3aa62.png?resizew=168)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7ddbb49c644bf06ccbad885ba2c84a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db26fcb4380a58ac02012e836e47d0a1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/a5efef69-8452-47f8-9267-86c994b3aa62.png?resizew=168)
A.三棱锥![]() ![]() ![]() |
B.过点P平行于面![]() ![]() ![]() |
C.当点P为![]() ![]() ![]() |
D.直线![]() ![]() ![]() |
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5 . 已知梯形
中,
,
,
,
,
是线段
的中点
将
沿
所在的直线翻折成四面体
,翻折的过程中下列选项错误的是
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a66200ae44919a57caf401a6d47737ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f976007b8d754ac3bf5793ed2fce37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a63e8a1e6411272e272c0ceee06e8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51fc7d1b20a1ce1761714c1733f0511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb961bd7db3adb76af2d4cedb611bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3182db896bc2462331796e2a6108363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba6fb5afc7fd86226985c0bd5e53b70.png)
![](https://img.xkw.com/dksih/QBM/2022/10/13/3086936201437184/3087431224401920/STEM/df144c563a014111926ba2fae4553021.png?resizew=4)
A.![]() ![]() |
B.当直线![]() ![]() ![]() ![]() |
C.四面体![]() ![]() |
D.四面体![]() ![]() |
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3卷引用:湖北省武汉市第三中学2022-2023学年高二上学期期中模拟数学试题
湖北省武汉市第三中学2022-2023学年高二上学期期中模拟数学试题湖南省益阳市2022-2023学年高二上学期10月联考数学试题(已下线)第二章 立体几何中的计算 专题六 几何体的外接球、棱切球、内切球 微点13 多边形折叠成二面角模型【基础版】
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解题方法
6 . 在三棱锥
中,
底面
,
,
,
为
的中点,球
为三棱锥
的外接球,
是球
上任一点,则三棱锥
体积的最大值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab2c27eac56fffa4cd7dbe1dcdf1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b7c1356f8e66f93d414b2a91e87cf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790c0a17ee2d7181ee95da741694bd1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae1de3f5eb55a078a2dc8d2a585b86a.png)
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7 . 如图,四棱锥
的底面
是菱形,其对角线
,
,
、
都与平面
垂直,
,
.则三棱锥
与四棱锥
公共部分的体积是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e5ba482836565abad208665cf7b9972.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d6bdfb0e1be5583e794ab614a8abe1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1364213f546b37f8764ddcb59e36ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93bc4c9dd737193f7acce692b23500d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52753d89bf58589e2e83b19bd3d140b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e5ba482836565abad208665cf7b9972.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/1/dfbacc32-81fc-40be-8d9a-0b6c406644f0.png?resizew=174)
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8 . 如图,在多面体
中,
为等边三角形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68453afa4b2af05bcd884f9a7c476398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12acc8f4f79ffc65f85bc405287a08c9.png)
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/27/531ec800-7d3c-45ab-abb4-a02ca88934f5.png?resizew=153)
(1)求证:平面
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/164a4df60a15587971e883cf557b5ce2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68453afa4b2af05bcd884f9a7c476398.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12acc8f4f79ffc65f85bc405287a08c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a06b5cd3910293ce3d671ba76e2553a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/27/531ec800-7d3c-45ab-abb4-a02ca88934f5.png?resizew=153)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0ca33e686caf0297d6cd27e9fa9079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8257b6bd25104e07b9ad935c0a3aac4.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678b28fddb166d90878d24d6e5481080.png)
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解题方法
9 . 斜三棱柱
的底面为边长是4cm的正三角形,侧棱长为3cm,侧棱
与底面相邻两边都成60°角.
(1)求证:侧面
是矩形;
(2)求这个棱柱的侧面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
(1)求证:侧面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0894e228b6a0085aa3a161b384c63d30.png)
(2)求这个棱柱的侧面积.
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解题方法
10 . 如图,正方体
的棱长为1,线段
上有两个动点
,且
,则下列结论中错误的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/11/72f7791c-b8ea-4428-9643-16976f38c18a.png?resizew=209)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4901a7eda97d6a307db76c4fb196ba3d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/11/72f7791c-b8ea-4428-9643-16976f38c18a.png?resizew=209)
A.![]() ![]() ![]() |
B.![]() |
C.三棱锥![]() |
D.![]() ![]() |
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