名校
1 . 已知正方体
的棱长为1,P是对角面
(包含边界)内一点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/31/6d929a77-227a-4a50-a5d6-997b59b4111e.png?resizew=161)
(1)求
的长度;
(2)是否存在点
,使得平面
平面
?若存在,求出点
的位置;若不存在,说明理由;
(3)过点
作平面
与直线
垂直,求平面
与平面
所成锐二面角的最小值,并求此时平面
截正方体
所得截面图形的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bf9ef324f1289e205e29fed105c38e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/036de574712cad14bddadf6653c7e714.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/31/6d929a77-227a-4a50-a5d6-997b59b4111e.png?resizew=161)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
(2)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
您最近一年使用:0次
解题方法
2 . 由曲线
围成的封闭图形绕
轴旋转一周所得的旋转体的体积为
;满足
的点
所组成的封闭图形绕
轴旋转一周所得的旋转体的体积为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/9/ff4c3def-8c4e-4174-9496-7c9e1a7b36c3.png?resizew=426)
(1)当
时,分别求出两旋转体的水平截面的面积
;
(2)求
与
的关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a16473364f2beecf1e4404987cd7e1c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ad9babbb0800e2fac1895399e24e01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0203b006524305c3d8ee0b6c34cd872b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/9/ff4c3def-8c4e-4174-9496-7c9e1a7b36c3.png?resizew=426)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbaa8af08dcb2eb604779d01a4cab47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
您最近一年使用:0次
名校
解题方法
3 . 如图所示,在直四棱柱
中,底面ABCD是等腰梯形,
,
,
,四边形
是正方形.
![](https://img.xkw.com/dksih/QBM/2022/5/24/2986420541005824/2987744622305280/STEM/0babbae5-66e1-4454-955f-aeecba309a60.png?resizew=245)
(1)指出棱
与平面
的交点E的位置(无需证明),并在图中将平面
截该四棱柱所得的截面补充完整;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12143a06ed24558d8cc7ad39961d3e1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82b724168afaee2ecddf97257180be18.png)
![](https://img.xkw.com/dksih/QBM/2022/5/24/2986420541005824/2987744622305280/STEM/0babbae5-66e1-4454-955f-aeecba309a60.png?resizew=245)
(1)指出棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b2213b575a7cfaffcdf91885005c7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36b2213b575a7cfaffcdf91885005c7d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8375f8f2a0dd3e0212ce52d334952c.png)
您最近一年使用:0次
2022-05-26更新
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752次组卷
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4卷引用:河南省平顶山市汝州市第一高级中学2022届高三下学期考前模拟考试理科数学试题