名校
1 . 如图所示,正方体
的棱长为1,线段
上有两个动点
,且
,则下列结论中正确的有( )
;
②三棱锥
的体积为定值;
③
的面积与
的面积相等;
④二面角
的正切值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f115f2683c0422042f1846450885e7fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589ddae20626f9aaac616d2a3b5d95bd.png)
②三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc3bf74119692ac98eb24fcfa2a3f9f.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2ea13010e2399194be2a681310543e.png)
④二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecd41f11a3360662c09b042a9f987e70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
A.1个 | B.2个 | C.3个 | D.4个 |
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解题方法
2 . 如图,已知
中
为直角,
是线段
上任意一点(不含端点),沿直线
将
折成
,所成二面角
的平面角为
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3818a2c9919d358b4c3713396093822b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/172f1b400d9ddec4ea01f6fd040b3802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff0a49b9a3976893039103a7ba3727e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa19f78fd19c8e5601bba0f52e438ca6.png)
A.![]() | B.![]() ![]() ![]() |
C.![]() | D.![]() ![]() ![]() |
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3 . 如图,在三棱锥
中,
平面
,平面
平面
,
,
.
;
(2)求二面角
的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56ee81929c987732fcb379802eeef7a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f5fc4ad65b723b6a8da4c8dac154e6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13d28cb7181257cf732af4b615fc47d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca6d1c5eace748465b2dad5065f5111c.png)
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4 . 在四面体
中,棱
的长为
,若该四面体的体积为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829678a17c4ba4653038502bf21d0f23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f83dbfddc6f98548699ed581e8c8608.png)
A.异面直线![]() ![]() ![]() | B.![]() ![]() |
C.点D到平面![]() ![]() | D.当二面角![]() ![]() |
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|
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3卷引用:辽宁省名校联盟2023-2024学年高二下学期3月联合考试数学试卷
名校
5 . 已知正方形
的边长为1,将正方形
绕着边
旋转至
分别为线段
上的动点,且
,若
,则
的最小值为( )
![](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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec3ad6ec7029b637ffdd5eab44ec80d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53a08d81353a3ea431787f550b9d9b7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a28ed244483ccc6728ebdc5e7fdc856.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc39144b305c67d44410d41053a1d28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/cb9bc368-3a2f-41be-82d5-a88c18c5225b.png?resizew=158)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
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3卷引用:吉林省通化市梅河口市第五中学2024届高三下学期开学考试数学试题
名校
6 . 如图,在三棱锥
中,平面
平面
为棱
上靠近点
的三等分点,且
为
的角平分线,则二面角
的平面角的正切值的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74684c76385a0240f1e9b7f22202ef12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fabb884dc5f9609de491245463bbe9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf29d07c3751c41ab3503065a5a5052e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/3/16513c35-d137-41b3-ad20-4b4258f1d346.png?resizew=154)
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2024-03-04更新
|
474次组卷
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3卷引用:湖南省三湘创新发展联合体2023-2024学年高三下学期2月开学统试数学试题
7 . 在如图所示的三棱锥
中,
分别是线段
的中点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/ddb31d53-420c-421d-ad70-a7d3e7e889dd.png?resizew=134)
(1)证明:直线
平面
;
(2)若二面角
的大小为
,求直线
和平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/358c6594ed1b0efc0415e8d64bbe8fa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28a77aa6c27acfffcc601d9ca7e6d4c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47f8c4ef0aee67b54282d9a6fa7714ea.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/ddb31d53-420c-421d-ad70-a7d3e7e889dd.png?resizew=134)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93cf663ee2bf1ac5c43f4306fa0cf250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/780d3f5f4c4419913c1232b7aae03ade.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107b87854ea594f77a40b25becd36020.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/588690c4a218025937357ffab8d63c7a.png)
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解题方法
8 . 已知:长轴与短轴长分别为
与
的椭圆围成区域的面积为
.现要切割加工一个底面半径为1、高为2的圆柱形零件(如图所示),截面经过圆柱的一个底面中心,并且与底面所成角为
.然后再对切割后得到的两个部件表面都刷上油漆,则所刷油漆的面积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/222ab5d8-7298-4502-b769-c5b95900135a.png?resizew=112)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/878e89b6eca35e34c863e832a2c661db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18436f0e2391b0ab7537a566fc28204c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/013f6e184e0f2db54e0398c79d9ee8ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/222ab5d8-7298-4502-b769-c5b95900135a.png?resizew=112)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 三棱锥
各顶点均在半径为2的球
的表面上,
,二面角
的大小为
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f17c2222ccbb93af7bc2e8c307c92ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b796bbaeb8450404c2d146283562006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
A.直线![]() ![]() ![]() |
B.三棱锥![]() ![]() |
C.点![]() ![]() |
D.点![]() ![]() |
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10 . 如图,在四棱柱
中,底面
和侧面
均是边长为2的正方形.
.
(2)若
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d56889f2417c8449b7ed31a03550d24.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fcb99b46d35b58383fb46737b99e8c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ee7e8d13fcdce579695d45a366eb7a3.png)
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|
603次组卷
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5卷引用:山东省济南第一中学等校2024届高三下学期阶段性检测(开学考试)数学试题
山东省济南第一中学等校2024届高三下学期阶段性检测(开学考试)数学试题四川省雅安市雅安中学等校联考2024届高三下学期开学考试数学(理)试题(已下线)8.6.2平面与平面垂直(已下线)专题3.8 立体中的夹角和距离问题-重难点突破及混淆易错规避(人教A版2019必修第二册)(已下线)重难点专题14 利用传统方法解决二面角问题-【帮课堂】(苏教版2019必修第二册)