名校
解题方法
1 . 如图所示的空间几何体是以
为轴的
圆柱与以
为轴截面的半圆柱拼接而成,其中
为半圆柱的母线,点
为弧
的中点.
平面
;
(2)当
,平面
与平面
夹角的余弦值为
时,求点
到直线
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15f3e3f310f6ec3f3a26498e7ee17a00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ee01e28681b584f85c8875f053b77b.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90131175c3fb6a3837a22d7d5bbc268d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83303d3784492506fc44f2b4d6b07bc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e322e0c87479bba874db9ae9ba36b5.png)
您最近一年使用:0次
2024-06-08更新
|
421次组卷
|
3卷引用:2024届福建省莆田市第一中学高三下学期5月模拟考试数学试题
名校
解题方法
2 . 如图,在直三棱柱
中,
,
分别为线段
,
上的点,且
平面
.
;
(2)当
为
的中点,
时,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/307807ee10071bafbe922eb18d2517d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb66e4fa5ca4231b8ce2490eeb192b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/489bc206882a18e50d4d5272e5b862ef.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3570a95f68349fcd9417fcda62e78e7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e04a0ba8fe0c0a240669fd793b7cb7.png)
您最近一年使用:0次
2024-06-08更新
|
1229次组卷
|
3卷引用:福建省莆田第一中学2023-2024学年高一下学期期中考试数学试题
福建省莆田第一中学2023-2024学年高一下学期期中考试数学试题(已下线)6.5.1直线与平面垂直-【帮课堂】(北师大版2019必修第二册)福建省福州市闽侯县第一中学2023-2024学年高一下学期第二次月考(5月)数学试题
名校
解题方法
3 . 在正三棱柱
中,D为棱
的中点,若
是面积为6的直角三角形,则此三棱锥
的体积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d021334737f555d75a65177f7ebebc81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/563ec242a8d49fe903d18d50dc716224.png)
您最近一年使用:0次
2024-05-11更新
|
268次组卷
|
4卷引用:福建省莆田市第二中学2023-2024学年高一下学期期中考试数学试题
福建省莆田市第二中学2023-2024学年高一下学期期中考试数学试题(已下线)6.6简单几何体的再认识-【帮课堂】(北师大版2019必修第二册)(已下线)6.6.1-2 柱、锥、台的表面积和体积-同步精品课堂(北师大版2019必修第二册)福建省宁德市福安市第一中学2023-2024学年高二下学期第三次月考数学试题
名校
4 . 如图,在四棱锥
中,四边形
是正方形,
,M为侧棱PD上的点,
平面
.
.
(2)若
,求二面角
的大小.
(3)在(2)的前提下,在侧棱PC上是否存在一点N,使得
平面
?若存在,求出
的值;若不存在,请说明理由.
![](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/267172a953126e44e36ab085165543ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb304d905125170bebfada27e7ed8960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccbd1316b9d1f0c1e71fd078deec61f6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d0710321d97361e5782124bbf7f0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f2d2fbc26a7be008f550b5828f615fe.png)
(3)在(2)的前提下,在侧棱PC上是否存在一点N,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f214481e6b23307a37940f6dd0313d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb304d905125170bebfada27e7ed8960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d7478de8e7971491d38e784529aff5.png)
您最近一年使用:0次
2024-05-08更新
|
1261次组卷
|
4卷引用:福建省莆田市2024届高三第四次教学质量检测(三模)数学试题
名校
5 . 在棱长为2的正方体
中,
在线段
上运动(包括端点),下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
A.存在点![]() ![]() ![]() |
B.不存在点![]() ![]() ![]() ![]() |
C.![]() ![]() |
D.以![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-03-13更新
|
632次组卷
|
4卷引用:福建省莆田市第二中学2023-2024学年高二下学期返校考试数学试卷
福建省莆田市第二中学2023-2024学年高二下学期返校考试数学试卷江苏省常州市2023-2024学年高三上学期期末学业水平监测数学试卷江苏省镇江市扬中市第二高级中学2023-2024学年高三下学期期初检测数学试题(已下线)专题06 立体几何 第二讲 立体几何中的计算问题(解密讲义)
名校
6 . 如图,在长方体
中,
,
,点
在线段
上.
(1)求证:
;
(2)当
是
的中点时,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d262480ffb55b7617f44b63f130c154a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/23/d5350071-8991-47ea-84cd-a9ad64d56ad1.png?resizew=150)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589ddae20626f9aaac616d2a3b5d95bd.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea84e9242d2667cd6a0f7436425ad418.png)
您最近一年使用:0次
2024-02-12更新
|
369次组卷
|
4卷引用:福建省莆田市锦江中学2023-2024学年高二下学期3月月考数学试题
福建省莆田市锦江中学2023-2024学年高二下学期3月月考数学试题陕西省西安市周至县2024届高三一模数学(理)试题(已下线)专题7.3 空间角与空间中的距离问题【九大题型】江苏省南京人民中学、海安实验中学与句容三中2023-2024学年高二下学期3月月考数学试题
名校
解题方法
7 . 在棱长为2的正四面体
中,点
是
所在平面内以
为左、右顶点,
为半短轴长的椭圆上的一动点(异于
两点).取
的中点为坐标原点
,以直线
为
轴,直线
为
轴建立平面直角坐标系
,若直线
和
的斜率分别为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92d82f6055983b8e9bb5a9cd8e09ebe5.png)
_____ ;
的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/c407500c3f3d395fdfdc366851ef3fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92d82f6055983b8e9bb5a9cd8e09ebe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
您最近一年使用:0次
名校
解题方法
8 . 如图,该几何体是由等高的半个圆柱和
个圆柱拼接而成,点
为弧
的中点,且
四点共面.
![](https://img.xkw.com/dksih/QBM/2023/12/18/3391983040479232/3392162142732288/STEM/ce7df57cd0eb402e878a1537e33cc0c1.png?resizew=150)
(1)求证:平面
平面
;
(2)若平面
与平面
所成二面角的余弦值为
,且线段
长度为4,求点
到直线
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63914ec190c89ea0b61348211b808673.png)
![](https://img.xkw.com/dksih/QBM/2023/12/18/3391983040479232/3392162142732288/STEM/ce7df57cd0eb402e878a1537e33cc0c1.png?resizew=150)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15f3e3f310f6ec3f3a26498e7ee17a00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ee01e28681b584f85c8875f053b77b.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90131175c3fb6a3837a22d7d5bbc268d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83303d3784492506fc44f2b4d6b07bc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
您最近一年使用:0次
名校
解题方法
9 . 在棱长为1的正方体
中,球
以点
为球心,棱
为半径,则平面
被球
截得的区域面积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775df7ba0dc94c15e9e706194a463f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
您最近一年使用:0次
名校
10 . 如图,在四棱锥
中,底面
是菱形,
,平面
平面
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/14/39bd5a0c-1527-4eb3-bd64-a0d8a1f1c53a.png?resizew=170)
(1)求证:
平面
;
(2)求平面
与平面
的夹角的余弦值.
![](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/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e1f990cb1de9609286fcd82d14cdf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/14/39bd5a0c-1527-4eb3-bd64-a0d8a1f1c53a.png?resizew=170)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e245440d3761fb4217eaa8dc303fa288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab5f236e0c248607721ff77b6ea8b6ee.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab5f236e0c248607721ff77b6ea8b6ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2023-11-19更新
|
350次组卷
|
3卷引用:福建省莆田五中、莆田八中、莆田十中、莆田侨中2023-2024学年高二上学期期末联考数学试卷