解题方法
1 . 如图,在斜三棱柱
中,
,且三棱锥
的体积为
.
(1)求三棱柱
的高;
(2)若平面
平面
为锐角,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131b887a0a088c760df5e17bd93bfe6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/861d61d2b7b16e12fd97f870fb3fa522.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/b7376265-a332-4131-9844-0dccb3b38662.png?resizew=168)
(1)求三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1111386161dc558c54930e35aa302737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32bbdf5dbf9df96742624ada95c36146.png)
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2024-02-24更新
|
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4卷引用:河南省周口市沈丘县第三高级中学2023-2024学年高二上学期期末数学试题
解题方法
2 . 已知四棱柱
在空间直角坐标系中,A在原点,
,四边形
是矩形.
(1)求三棱锥
的体积;
(2)求
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5ac0b303ec6ec19cf206100f54aa1f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/27/7122f987-9814-41d7-87b5-d997c805056a.png?resizew=232)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b0567b68ad33a371b2427de134a3ea5.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
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2023-09-26更新
|
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2卷引用:河南省周口市项城市莲溪高级中学等5校2022-2023学年高二下学期2月月考理科数学试题
3 . 如图,已知圆锥的顶点为P,底面圆
的直径AB长为4,点C是圆上一点,
,点D是劣弧
上的一点,平面
平面
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/21/d2732e5a-b0a6-4afa-8de8-fa4e48bb1e41.png?resizew=163)
(1)证明:平面
平面POD.
(2)当三棱锥
的体积为
时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bfb836792b1eebfbd08a6f46fae580e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/667349d99185bb045030b733352ff7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c762937111e04018cad6b507a7dedc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baceb049bf16ed0fd33639fdda0ec5ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c29f3123f57b56444be9bc048eacc82.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/21/d2732e5a-b0a6-4afa-8de8-fa4e48bb1e41.png?resizew=163)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7392e9e2da5a0e9ecab0f79992656328.png)
(2)当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b2a4541d85e8710408c45c99950b6af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d599cb4a589f90b0205f24c2e1fa021e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0297943fae12e34fab38c541002b15.png)
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2卷引用:河南省项城市第三高级中学2022-2023学年高二上学期第一次调研考试数学试题
4 . 如图,已知正方体
的棱长为1,E为CD的中点,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db3ef97d64e58d311019b70fe5e2cc0d.png)
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2023-01-03更新
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6卷引用:河南省周口市太康县第三高级中学2022-2023学年高二上学期12月月考理数试题
名校
解题方法
5 . 如图,在四棱锥
中,底面ABCD是直角梯形,
,
,
,
,
,平面
平面ABCD,且
,E为BC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/27/43c6a96b-3efe-43db-8021-ce0c47d21dd0.png?resizew=186)
(1)证明:平面
平面PBD.
(2)若四棱锥
的体积为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d783fe7f3ce673d5d21281174e7a7968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32e1b499d6b25ee132abcdd3f3cd288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c383691e8d740830a865b12d66f7633.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/27/43c6a96b-3efe-43db-8021-ce0c47d21dd0.png?resizew=186)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d96357a07048ba79b8c84097d359d9.png)
(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c20567d122853e7c3119a1749ca8ccc4.png)
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2022-04-26更新
|
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4卷引用:河南省周口市恒大中学2023-2024学年高二下学期开学考试数学试题
名校
解题方法
6 . 如图所示,在四棱锥
中,底面
为直角梯形,平面
平面
,
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2022/3/7/2931316583587840/2932502327058432/STEM/5b6d3ec2-76e6-4d7c-af7e-b090164fea99.png?resizew=180)
(1)求证:
,并且求三棱锥
的体积;
(2)求直线
与平面
所成角的正弦值.
![](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/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b0e30c61f4433ca0d6b7c30d82632a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678069acbf21579b42a786385b154c8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e628d8d153b597967cbcb6e02250b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/2022/3/7/2931316583587840/2932502327058432/STEM/5b6d3ec2-76e6-4d7c-af7e-b090164fea99.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d84733f9dc908ceb11459cc2aed580ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddfe0ccf24d760c77535a70c92dad145.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
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2卷引用:河南省周口市周口恒大中学2023-2024学年高二上学期9月月考数学试题
名校
解题方法
7 . 如图,在三棱柱
中,已知
,
,点
在底面
上的投影是线段
的中点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/17/8c67e2f9-f104-45cb-a802-20c6670fe650.png?resizew=213)
(1)证明:在侧棱
上存在一点
,使得
平面
,并求出
的长;
(2)求三棱柱
的侧面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c462dcc5fba8c0a19d8b69366e01ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/17/8c67e2f9-f104-45cb-a802-20c6670fe650.png?resizew=213)
(1)证明:在侧棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9de7ea432599108b34a0ccaa0f2c75e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58cc6184b191e6da43911e701121517e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(2)求三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
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2017-02-16更新
|
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5卷引用:【全国市级联考】河南省周口市2017-2018学年高二下学期期末考试数学(文)试题