名校
1 . 如图,在三棱台
中,
,平面
平面
,
.
平面
;
(2)若三棱锥
的体积为
,求平面
与平面
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/822ba132ca9dd0d4a050659aef3c9b26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a2e10a5aebe40a9018d5ee3ade7af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1638b1b615ff368c456cc1fbbcd0464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a50eda31bbc3d40f0b305d4ac673fc21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(2)若三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38593653bedb845ecfa820806a29a1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
您最近一年使用:0次
2024-05-13更新
|
860次组卷
|
3卷引用:安徽省合肥市一六八中学2024届高三下学期最后一练数学试题
名校
2 . 如图,在三棱锥
中,
,平面
平面
,则三棱锥
外接球的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94be5939e90b206cb6233321fe214bc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17580410bf63dba4fe164265afaac4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
3 . 如图,在四棱锥
中,正方形
的边长为2,平面
平面
,且
,
,点
分别是线段
的中点.
(1)求证:直线
平面
;
(2)求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1e038b4e76b3a368731d3331522b8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5352d28609d1b3d09a0a29d023d1bb72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d900531973c546625694146fa1509ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29e240a6378adf6d23ebf9cc710c9bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a003de8409231a347edebc8284be186c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85de410d85be189dfa5aabb33410b896.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/28/78915c23-3509-4e01-a87e-c35695e43029.png?resizew=127)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c27a8fd3bf5b89a16dbbe1a8230653c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0e57a13c665af88f326c9890072bf73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
您最近一年使用:0次
2023-05-26更新
|
843次组卷
|
3卷引用:安徽省合肥市第五中学2022-2023学年高二下学期学科教学评价数学试卷
4 . 如图所示,在四棱锥
中,
为等腰直角三角形,
,平面
平面ABCD,
,
,
.
(1)求证:平面
平面PCD;
(2)若点E为PB的中点,F为CD的中点,点M为AB上一点,当
时,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e78042a384255038de485fd7bc0839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7e4d805457ae6da85e67a71980adef4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4ab7e657f01bdfa235f8c4d6681d13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cd60919c09876f29ff699b790f701f0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/21/2bc0f772-bc19-4e07-a742-a86f8892264d.png?resizew=149)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
(2)若点E为PB的中点,F为CD的中点,点M为AB上一点,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b87516d02001590a14b4df66bbd469c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dfcb4b832b1fd021d2508f354f5da36.png)
您最近一年使用:0次
名校
5 . 如图,在斜三棱柱
中,平面
平面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/11/a8b0db79-4002-4c93-a0ee-48bee3eeebea.png?resizew=189)
(1)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd11d3ed6d1ee395217cdbc38dd1d399.png)
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df00cdf77ed39ca5a0b305861a693142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2450add63e7630e76e1d736d03c73a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/11/a8b0db79-4002-4c93-a0ee-48bee3eeebea.png?resizew=189)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd11d3ed6d1ee395217cdbc38dd1d399.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91cbafbd47a57b0a24799ca61af682f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b4d6f55cb2000cc7b578475fcb3baba.png)
您最近一年使用:0次
2023-03-10更新
|
474次组卷
|
2卷引用:安徽省合肥市中锐学校2024届高三上学期期末数学试题
名校
6 . 四棱锥
中,四边形
为梯形,其中
,
,
,平面
平面
.
(1)证明:
;
(2)若
,且
与平面
所成角的正弦值为
,点
在线段
上且满足
,求平面
与平面
所成的锐二面角的余弦值.
![](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/68d31600cba2d5256c7e78b6122d6755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec2d5ab801f2a84b78139b0ea2c5032b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ec435aa1401dbce7863b531bf2f3e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/31/6aa23a73-9b96-42af-8dc0-3a62ce5b7083.png?resizew=150)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9104a1941e557a85fd1496bc2b9be297.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d0710321d97361e5782124bbf7f0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d9662368fd788afb77b79035cdd268b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/832b1cdf04126ed1beb48eb581f4234b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac93e58e9bba899df62a4cda5f1a5ca2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
名校
7 . 如图,三棱锥
中,
,平面
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/049bcfd0-fa83-46d4-8cd5-f34db022679e.png?resizew=203)
(1)求证:
平面
;
(2)若点
在线段
上,直线
与直线
所成的角为
,求平面
与平面
所成的锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1777619bfe1167d487f3a8507fba7fbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee98db8495cf1f203abe99795102e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069fb06e0428a1cb2b4ce4c17eeab7fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c075a9952e8a47ae7a39fba0e5ec4b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b1b01db19ea917c24cff42156a2412.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/23/049bcfd0-fa83-46d4-8cd5-f34db022679e.png?resizew=203)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e6956d407141c5d3a08f840ffa8b41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252053b853152bd294a8315debd00b92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20b69099d2b74ffbb1f365e1468bd8fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422210c777ac0d625bbd81cc7601bf9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
您最近一年使用:0次
2022-10-19更新
|
635次组卷
|
6卷引用:安徽省合肥市第十中学2022-2023学年高三上学期第四次段考数学试题
8 . 如图,在四棱锥
中,底面
是边长为1的正方形,
底面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/9/c11cff88-3db6-4c9c-b63b-8e3d2365c4e9.png?resizew=166)
(1)证明:平面
平面
;
(2)点M在平面
内,直线
平面
,求四棱锥
的体积.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829f9180ddd9aa1a0ee0dc520f4e0b5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/9/c11cff88-3db6-4c9c-b63b-8e3d2365c4e9.png?resizew=166)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)点M在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4117625867a74cd022584500c76deca.png)
您最近一年使用:0次
2022-05-31更新
|
587次组卷
|
3卷引用:安徽省合肥一六八中学2022届高三下学期5月最后一卷文科数学试题
名校
9 . 梯形ABCD中,
,
,
,
,将
沿AC折起,使平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/d2d3771f-6063-4ecb-89a1-bda4740429ec.png?resizew=325)
(1)证明:
平面
;
(2)AC中点为M,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4795ee1f96b430529934e2231b38885d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/633bf2de732ae51fc06ef3d559915da0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/644f63756fe9251e65cc14e1ce9723d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8ff58f671a287701011a1b31e67e28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/d2d3771f-6063-4ecb-89a1-bda4740429ec.png?resizew=325)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)AC中点为M,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64785e4401e1d79632e360fd3626ed62.png)
您最近一年使用:0次
2022-04-17更新
|
461次组卷
|
2卷引用:安徽省合肥市第七中学2022届高三下学期二模(一)理科数学试题
10 . 刍甍(chú méng)是中国古代数学书中提到的一种几何体.《九章算术》中有记载“下有袤有广,而上有袤无广”,可翻译为:“底面有长有宽为矩形,顶部只有长没有宽为一条棱.”如图,在刍甍
中,四边形
是正方形,平面
和平面
交于
.
![](https://img.xkw.com/dksih/QBM/2022/2/27/2913341073735680/2925903899746304/STEM/fe85615f-911c-442b-9074-ae46dcc43593.png?resizew=176)
(1)求证:
平面
;
(2)若
,
,
,
,再从条件①,条件②,条件③中选择一个作为已知,使得刍甍
存在,并求平面
和平面
夹角的余弦值.
条件①:
,
;
条件②:平面
平面
;
条件③:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ba3f676fda6a2aaaa55c9f32874a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10fc7991ea17d54ff5f4445ac5699463.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://img.xkw.com/dksih/QBM/2022/2/27/2913341073735680/2925903899746304/STEM/fe85615f-911c-442b-9074-ae46dcc43593.png?resizew=176)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe43b94a84f969479064474603599797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ba3f676fda6a2aaaa55c9f32874a51.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeedb5f361a1baff6338436fff6c471d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/869dbfaf24d441c4ce3a2b8db86cd2e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678988261e6fd7c4f1199c0204a8045d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ba3f676fda6a2aaaa55c9f32874a51.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8baaea02eaa7e473fb2a8f84ba575c25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd40e867f1d3377cf4fb9ae730d04cf7.png)
条件②:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c1acdd27cebb11e0266464b03b3afb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
条件③:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec2af539ca4fdc2fa94d4986537b6598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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2022-02-28更新
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4卷引用:安徽省合肥一六八中学2021-2022学年高二上学期第三次月考数学试题