名校
1 . 四棱锥
中,
平面
,四边形
为菱形,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/23/84289b76-d861-4559-8c82-87b8a0b0cf55.png?resizew=201)
(1)求证:平面
平面
;
(2)求
与平面
所成的角的正切值;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd9cba0ec6619ed299ee9ab9cdfe482b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3e076b62ef0f326e366b6d366d68812.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/23/84289b76-d861-4559-8c82-87b8a0b0cf55.png?resizew=201)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22583ac400216f5aa56a84284efe4b12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
2022-09-22更新
|
1513次组卷
|
9卷引用:上海市复旦大学附属中学2023届高三上学期9月月考数学试题
上海市复旦大学附属中学2023届高三上学期9月月考数学试题(已下线)第03讲 直线、平面平行垂直的判定与性质(练)(已下线)第04讲 空间直线、平面的垂直 (高频考点—精讲)-2(已下线)专题15 立体几何(讲义)-2四川省绵阳市南山中学2022-2023学年高二上学期入学考试数学试题四川省南充市南充高级中学2022-2023学年高二上学期期中数学试题江苏省徐州市运河中学2022-2023学年高一下学期第三次学情检测数学试题湖北省仙桃荣怀学校2022-2023学年高二下学期第一次诊断考试数学试题四川省南充市南充高级中学2022-2023学年高二上学期期中考试数学文科试题
2 . 如图,已知正三棱柱
中,
.D是棱
上一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/0156343d-31cc-4d83-b088-6f451f269f64.png?resizew=151)
(1)若
,求直线BD与平面ABC所成角的大小;
(2)若D是
中点,求点A到平面BCD的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92105835f8075cb75dff244e908370b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/13/0156343d-31cc-4d83-b088-6f451f269f64.png?resizew=151)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c37515c01f1b2560e7b5ba92ede076d.png)
(2)若D是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
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3 . 如图,圆锥的底面半径
,高
,点
是底面直径
所对弧的中点,点
是母线
的中点.求:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/461f5397-a3b1-4a54-8920-6454e69163e4.png?resizew=112)
(1)该圆锥的表面积;
(2)直线
与平面
所成角的大小(结果用反三角函数值表示).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9774f83067ed956a551bc41adcce0469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f091d853ef8f4133dfa73d7b9622cee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/461f5397-a3b1-4a54-8920-6454e69163e4.png?resizew=112)
(1)该圆锥的表面积;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
4 . 如图,四棱锥
的底面是矩形,
底面
,
,
,四棱锥
的体积为
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/29/9a047b33-4898-4109-96ca-4c18832dcb25.png?resizew=284)
(1)求异面直线
与
所成的角;
(2)求直线
与平面
所成的角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f144992e1cbee34868abce1e5ad38c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36d74ef32584586ec4857acd0a3f4fe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/29/9a047b33-4898-4109-96ca-4c18832dcb25.png?resizew=284)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
您最近一年使用:0次
5 . 如图,直角边长为
的等腰直角三角形
及其内部绕
边旋转一周,形成一个圆锥.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/25/4172f43c-76e0-4024-b27d-3088a7e84ba0.png?resizew=195)
(1)求该圆锥的侧面积
;
(2)三角形
绕
逆时针旋转
到
,
为线段
中点,求
与平面
所成角的大小.(结果用反三角函数值表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/25/4172f43c-76e0-4024-b27d-3088a7e84ba0.png?resizew=195)
(1)求该圆锥的侧面积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(2)三角形
![](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/b1ad72d7565699d1ebb741eb0ce12bac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef671ff46a372d5351b8c2f9eb26b48.png)
您最近一年使用:0次
2022-06-23更新
|
418次组卷
|
6卷引用:上海市黄浦区2022届高考二模数学试题
上海市黄浦区2022届高考二模数学试题(已下线)2023年上海高考数学模拟卷01第11章 简单几何体(B卷·能力提升练)-【单元测试】2022-2023学年高二数学分层训练AB卷(沪教版2020必修第三册)(已下线)第20讲 空间向量与立体几何-3(已下线)专题11空间向量与立体几何必考题型分类训练-2(已下线)第3章 空间向量及其应用(基础、常考、易错、压轴)分类专项训练(原卷版)
6 . 已知圆锥的顶点为
,底面圆心为
,母线
的长为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/24/e75be07e-ee9c-4019-8910-38c28c7d419e.png?resizew=228)
(1)若圆锥的侧面积为
,求圆锥的体积
(2)
是底面圆周上的两个点,
,
为线段
的中点,若圆锥的底面半径为2,求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/24/e75be07e-ee9c-4019-8910-38c28c7d419e.png?resizew=228)
(1)若圆锥的侧面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/511950f018a3e8b9a21ef8246007c0d5.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ccc37b189fa2cbc269ca0b233dac37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fddbb7f29e8672f34941fe70b0a1e45f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97fa483ce5e3575ff399722caba7b943.png)
您最近一年使用:0次
7 . 三棱锥
及其三视图中的主视图和左视图如下图所示.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/19/6202fb91-6125-407a-80fe-1770d81b9f02.png?resizew=377)
(1)求直线
与平面
所成角;
(2)求点
到平面
距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/19/6202fb91-6125-407a-80fe-1770d81b9f02.png?resizew=377)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
名校
8 . 圆柱的轴截面ABCD是正方形,E是底面圆周上一点,DC与AE成60°角,
.
(2)求点B到平面AEC的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
(2)求点B到平面AEC的距离.
您最近一年使用:0次
2022-05-05更新
|
585次组卷
|
7卷引用:上海市曹杨第二中学2023届高三上学期高考模拟(11月)数学试题
上海市曹杨第二中学2023届高三上学期高考模拟(11月)数学试题上海市闵行区闵行中学2024届高三上学期12月月考数学试题上海市进才中学2021-2022学年高二下学期期中数学试题(已下线)第07讲 线面角(核心考点讲与练)-2022-2023学年高二数学考试满分全攻略(沪教版2020必修第三册)(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)(已下线)期中模拟预测卷03(测试范围:选修一+选修二)-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)(已下线)核心考点05 空间向量及其应用(2)
9 . 如图,在四棱台
中,
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/5/1/2970126163312640/2972724026155008/STEM/dd8cd43bebb84bdb9477c603d74f6cce.png?resizew=247)
(1)证明:
;
(2)若
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a0c3a4e61b97fa9bc58f3179fc2958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7720a24ccafd483cffe43b95be4ee20d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97d0adb7498ebd1cef04f3ed13238130.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab815649946f118c3729cd792b706dac.png)
![](https://img.xkw.com/dksih/QBM/2022/5/1/2970126163312640/2972724026155008/STEM/dd8cd43bebb84bdb9477c603d74f6cce.png?resizew=247)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff461dfa42284b4c7e282d41c87d810.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26587499b7c46239dc138d34fd3894f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a39cf1a9eedda28c63f13ea478ec6b.png)
您最近一年使用:0次
2022-05-05更新
|
478次组卷
|
2卷引用:上海市2023届高三上学期二模暨秋考模拟1数学试题
解题方法
10 . 如图,已知
为圆柱
的底面圆
的一条直径,
为圆周上的一点,
,
,圆柱
的表面积为
.
![](https://img.xkw.com/dksih/QBM/2022/4/28/2967900906315776/2968436869799936/STEM/7a3a128c565b41f690a240a800effd64.png?resizew=199)
(1)求三棱锥
的体积;
(2)求直线
与平面
所成的角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9774f83067ed956a551bc41adcce0469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8db0f7e87f1cb39e188ec4d9803b6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e0166cef87d437ba03524bbdb61288.png)
![](https://img.xkw.com/dksih/QBM/2022/4/28/2967900906315776/2968436869799936/STEM/7a3a128c565b41f690a240a800effd64.png?resizew=199)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5495a154d006c33979813b86924dc0f9.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a571745474520e3db9cb68c76585f63.png)
您最近一年使用:0次