名校
1 . 如图,在三棱柱
中,平面
平面
,
,过
的平面与
分别交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/14/9cfa1401-dba7-4adf-8ade-288c789e11a6.png?resizew=174)
(1)证明:四边形
为平行四边形;
(2)若
,则当
为何值时,直线
与平面
所成角的正弦值最大?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eff0db05826cbff651faf0144904b32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/665d44844d2b582e965128979a6f7091.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ba9574b2a856772570046d87a6242be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8db1db021a0cb0c7f301f6760258689d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0ae07505d28385b5ae7fa6769e6f91b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/14/9cfa1401-dba7-4adf-8ade-288c789e11a6.png?resizew=174)
(1)证明:四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35e2d45fd8c3d3d809571ce6d3b81271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
您最近一年使用:0次
2024-04-10更新
|
996次组卷
|
3卷引用:江西省南昌市第十九中学2024届高三下学期第二次模拟考试数学试题
2 . 已知空间中两条不同的直线
和两个不同的平面
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
A.若![]() ![]() ![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
名校
解题方法
3 . 如图,四棱锥
中,
,
,
,平面
平面
.
;
(2)若
,M是
的中点,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6a2b112facda441f4e34bf5c145fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0642d7f4f43b9d65aa8cb45157e6ef12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e4b16c2c6c9bd089da78122e9d2511.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96ece472b33e9c4be953068aa18724df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/691094b5155cf16e2dc87b74cbb45270.png)
您最近一年使用:0次
2024-02-04更新
|
1241次组卷
|
6卷引用:江西省南昌市第二中学2024届高三“九省联考”考后适应性测试数学试题(四)
江西省南昌市第二中学2024届高三“九省联考”考后适应性测试数学试题(四)四川省成都市第七中学2023-2024学年高三上学期期末考试文科数学试卷四川省绵阳南山中学2023-2024学年高三下学期入学考试文科数学试题(已下线)第07讲 空间直线﹑平面的垂直(二)-《知识解读·题型专练》(已下线)11.4.2平面与平面垂直-同步精品课堂(人教B版2019必修第四册)(已下线)专题01 高一下期末真题精选(2)-期末考点大串讲(人教A版2019必修第二册)
名校
解题方法
4 . 设直线
与球
有且只有一个公共点
,从直线
出发的两个半平面
截球
的两个截面圆的半径分别为1和
,二面角
的平面角为
,则球
的表面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d49f8a63ddbca52039fa9ab44cda6b29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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名校
解题方法
5 . 四棱锥
,底面
为矩形,
,
,
.
;
(2)设
与平面
所成的角为
,求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91711f305a9eed9a6686b1344e8ed562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b124c5256b5ad2f37d3dc806e866ae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d79e7020414add95907e061df505ef0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ccd5c41c921836b50f8e18abfdc5df3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
您最近一年使用:0次
名校
解题方法
6 . 已知四棱锥
的底面
是矩形,其中
,平面
平面
,
为等边三角形,则四棱锥
的外接球体积为( )
![](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/8716b5aad93d97ca1c3791b9c717cc0d.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/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-07-05更新
|
199次组卷
|
2卷引用:江西省南昌市第十九中学2024届高三上学期11月期中考试数学试题
名校
解题方法
7 . 已知四棱锥
的底面是正方形,且
,点
在底面上的射影在正方形
内,且
与平面
所成角的正切值为
.
(1)若
分别是
的中点,求证:点
在平面
内的射影
在线段
上,并求出
的值;
(2)若
是棱
的中点,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc91898ecb0b8c09d53dba44e9e39aa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/17e86bb45af21ce92699bd0bd0f784b3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/2/72740f67-f3a8-477a-8aab-961749aab46e.png?resizew=176)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e83fd42df335c85bf92b7961b9851977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba48366317ebea1c9dd5e4e67e03092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab2edb70a0195b14fedcfa7b64ecb6f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053932dc8c5eebbc739256cb4de6c71d.png)
您最近一年使用:0次
8 . 如图,在四棱锥
中,底面
是边长为4的菱形,
,
,点E在线段
上,
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/24/364e7f96-352b-4dec-a8bd-3f5a023f26d7.png?resizew=191)
(1)求
;
(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/5918807712bab71325f3a79661d2ea4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83640592853a53872d7af69c0cffc1bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddbb52f9b226b1db3f6f9f055948bd38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/24/364e7f96-352b-4dec-a8bd-3f5a023f26d7.png?resizew=191)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4d41989d897ddb0fe7aa59f3beaabf9.png)
您最近一年使用:0次
名校
解题方法
9 . 在多面体
中,平面
平面
,四边形
为直角梯形,
,
为
中点,且点
满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/9/00fd4f4e-ba12-46ac-8e5f-f5d78f1b4a43.png?resizew=145)
(1)证明:
平面
;
(2)求多面体
的体积最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c99e6d75d606b5cae9392ecca969200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9d54cbbf601f4583659771eb534997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f41bf5ba46efcc6dbc8e527a94ed2343.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08dcecfcdc15fbd0fc57f5f1d8a6f0d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21037e170bdbb322558e79c40c00b454.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44e27e7ca8862c8843d15080709a88fc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/9/00fd4f4e-ba12-46ac-8e5f-f5d78f1b4a43.png?resizew=145)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf60ad9db3411f35704fa88d86bfef5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
您最近一年使用:0次
2023-03-02更新
|
462次组卷
|
3卷引用:江西省南昌市第十中学2023届高三第一次模拟数学(文)试题
名校
10 . 如图1,在边长为2的菱形
中,
,点
分别是边
上的点,且
,
.沿
将
翻折到
的位置,连接
,得到如图2所示的五棱锥
.
平面
?证明你的结论;
(2)若平面
平面
,记
,
,试探究:随着
值的变化,二面角
的大小是否改变?如果改变,请说明理由;如果不改变,请求出二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/481e426224c3a3ce9bb5a731eed81c40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d07d7a3d7f32ce2b4baa1f9346dc7e3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e06b8bc2571146b241e6028a742e3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12225a1a1eda07908309f8100cc34726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b99271fe84300da304205280de1b63e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43d865d5674e5c4e15946e45dce8dc2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4180c271831327644dc83240b715b5.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9ab73fd4ddacc0c1524f8d742c7dcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e470e983b075e6442750758e11081e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f342c5e045dba220e9c37b0bb769e4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb6bf23a5a12e1ba5413594d7b1a57c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6e39e62dad9881e30ac929c1f2958e.png)
您最近一年使用:0次
2022-12-21更新
|
441次组卷
|
4卷引用:江西省南昌市第十九中学2022-2023学年高三下学期第一次月考理科数学试卷