名校
1 . 如图,正三棱柱
中,
,
,E、F分别为棱
和
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/9/ff330200-79d5-4b4a-b108-df1523c5aef5.png?resizew=146)
(1)求直线
与平面
所成角的正弦值;
(2)在线段
是否存在一点M,使得平面
∥平面
?若存在,请指出并证明;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db57eca2a7cbd91bc57372592580a76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/9/ff330200-79d5-4b4a-b108-df1523c5aef5.png?resizew=146)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed4cba9d2412e4a28f8740bddd5738d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
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2022-05-05更新
|
864次组卷
|
4卷引用:专题10 立体几何的综合问题-2021-2022学年高一数学下学期期末必考题型归纳及过关测试(人教A版2019)
(已下线)专题10 立体几何的综合问题-2021-2022学年高一数学下学期期末必考题型归纳及过关测试(人教A版2019)(已下线)专题09 立体几何中的角度、距离、体积问题-2021-2022学年高一数学下学期期末必考题型归纳及过关测试(人教A版2019)河南省开封市五县2021-2022学年高一下学期期中考试数学试题重庆市中山外国语学校2022-2023学年高一下学期5月月考数学试卷
名校
2 . 已知四棱锥
的底面是边长为2的菱形,
底面
.
![](https://img.xkw.com/dksih/QBM/2022/5/3/2971467522613248/2972829229432832/STEM/59d7d6e6073141fd9ad4fe4d23e58024.png?resizew=244)
(1)求证:
平面
;
(2)已知
,
(ⅰ)当
时,求直线
与
所成角的余弦值;
(ⅱ)当直线
与平面
所成的角为
时,求四棱锥
的体积.
![](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://img.xkw.com/dksih/QBM/2022/5/3/2971467522613248/2972829229432832/STEM/59d7d6e6073141fd9ad4fe4d23e58024.png?resizew=244)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bec03e804f0cea1db5cde2aa185056a.png)
(ⅰ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d6bdfb0e1be5583e794ab614a8abe1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
(ⅱ)当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
2022-05-05更新
|
3103次组卷
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5卷引用:期末押题预测卷01
(已下线)期末押题预测卷01广东省广州市白云中学2021-2022学年高一下学期期中数学试题广东省茂名市信宜市第二中学2022-2023学年高一下学期期末数学试题江苏省盐城市响水中学2021-2022学年高二下学期第二次学情分析考试数学试题(已下线)第02讲 玩转立体几何中的角度、体积、距离问题-【暑假自学课】2022年新高二数学暑假精品课(苏教版2019选择性必修第一册)
名校
解题方法
3 . 如图,在直三棱柱
中,
,
,
,点
是侧棱
上的一个动点,则下列判断正确的是( )
![](https://img.xkw.com/dksih/QBM/2022/5/2/2970612790157312/2971987736903680/STEM/c610efb823174bc297ec5c994ebd6463.png?resizew=167)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/2022/5/2/2970612790157312/2971987736903680/STEM/c610efb823174bc297ec5c994ebd6463.png?resizew=167)
A.![]() |
B.![]() ![]() |
C.直线![]() ![]() ![]() |
D.存在点![]() ![]() ![]() |
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4 . 如图,正方体
的棱长为1,E,F,G分别为BC,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
的中点,则下列结论正确的个数是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/18/ad7b9d21-3ea0-45b8-b20f-df154a1fd0fb.png?resizew=196)
①直线
与直线DC所成角的正切值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
②直线
与平面AEF不平行
③点C与点G到平面AEF的距离相等
④平面AEF截正方体所得的截面面积为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4700efcb84c4027ce7a50af0d5212fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa07e3638259f1e0629d2ed724d6932.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/18/ad7b9d21-3ea0-45b8-b20f-df154a1fd0fb.png?resizew=196)
①直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04777f3f4661fa1c08a1cc0dfb807c7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
②直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04777f3f4661fa1c08a1cc0dfb807c7d.png)
③点C与点G到平面AEF的距离相等
④平面AEF截正方体所得的截面面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4700efcb84c4027ce7a50af0d5212fc.png)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
名校
5 . 某班级到一工厂参加社会实践劳动,加工出如图所示的圆台O1O2,在轴截面ABCD中,AB=AD=BC=2cm,且CD=2AB,下列说法正确的有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/17/b9424adf-194a-4d18-93ab-87dd767093eb.png?resizew=321)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/17/b9424adf-194a-4d18-93ab-87dd767093eb.png?resizew=321)
A.该圆台轴截面ABCD面积为![]() ![]() |
B.该圆台的体积为![]() ![]() |
C.该圆台的母线AD与下底面所成的角为30° |
D.沿着该圆台表面,从点C到AD中点的最短距离为5cm |
您最近一年使用:0次
2022-09-15更新
|
983次组卷
|
15卷引用:广东省广州市白云区、海珠区2020-2021学年高一下学期期末数学试题
广东省广州市白云区、海珠区2020-2021学年高一下学期期末数学试题(已下线)期末模拟卷-2021-2022学年高一数学链接教材精准变式练(人教A版2019必修第二册)(已下线)专题10 立体几何的综合问题-2021-2022学年高一数学下学期期末必考题型归纳及过关测试(人教A版2019)湖北省武汉市江岸区2021-2022学年高一下学期期末数学试题内蒙古自治区呼和浩特市内蒙古师范大学附属中学2022-2023学年高一下学期期末数学试题湖南省长沙市长郡中学2021-2022学年高一下学期期末综合复习数学试题(已下线)第九章 立体几何专练3—简单几何体的表面积与体积1-2022届高三数学一轮复习(已下线)8.3 简单几何体的表面积与体积-2021-2022学年高一数学10分钟课前预习练(人教A版2019必修第二册)(已下线)第08讲 简单几何体的表面积和体积(核心考点讲与练)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)(已下线)第8.3讲 简单几何体的表面积与体积-2021-2022学年高一数学链接教材精准变式练(人教A版2019必修第二册)浙江省宁波市咸祥中学2021-2022学年高一下学期期末数学试题安徽省滁州市定远县育才学校2021-2022学年高一下学期期中考试数学试题4.5.2 几种简单几何体的体积湖北省十堰市丹江口市第一中学2021-2022学年高二上学期9月月考数学试题福建省厦门双十中学2021-2022学年高一下学期期中考试数学试题
解题方法
6 . 长方体
,
,
,若直线
与平面
所成角的正弦值为
,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1d20564320dc28e1b429ec389ccf309.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a88b719166fcc1431f876bc8c5656c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/756d4d8a7051af5dae3ef56cb9e47c5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2122e3f1e76a635e58e4d54aa594c552.png)
![](https://img.xkw.com/dksih/QBM/2022/4/26/2966351585132544/2970693335785472/STEM/758ba9e4-0fe7-4bfb-bd86-a1476f14f539.png?resizew=160)
您最近一年使用:0次
2022-05-02更新
|
504次组卷
|
4卷引用:专题09 立体几何中的角度、距离、体积问题-2021-2022学年高一数学下学期期末必考题型归纳及过关测试(人教A版2019)
(已下线)专题09 立体几何中的角度、距离、体积问题-2021-2022学年高一数学下学期期末必考题型归纳及过关测试(人教A版2019)江苏省仪征市精诚高级中学2021-2022学年高一年级5月月考数学试题浙江省温州市知临教育集团2021-2022学年高一下学期期中数学试题浙江省金华市曙光学校2021-2022学年高一下学期第二次阶段考试数学试题
7 . 如图所示,在正方体
中,M,N分别为棱
,
的中点,则下列四个结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/4/c3aa718d-4bed-49a8-a09d-de7bea22e06f.png?resizew=184)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e97fcdcfd6183b976a61ef3222c607.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/4/c3aa718d-4bed-49a8-a09d-de7bea22e06f.png?resizew=184)
A.直线AM与![]() |
B.直线AM与BN是平行直线 |
C.直线AM与BN所成角的余弦值为![]() |
D.直线AM与平面![]() ![]() |
您最近一年使用:0次
8 . 如图,在五棱锥
中,
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/4/22/2963685198184448/2964949001191424/STEM/a728d45c-04c3-4649-bd1f-1353a526477c.png?resizew=135)
(1)求二面角
的大小;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be89b9d1709d7974a108142c5fa2ccec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32906cc874b3f574f3142cd9f50d7516.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbbbcd232d0ab87ef2dbaeb43fff73d1.png)
![](https://img.xkw.com/dksih/QBM/2022/4/22/2963685198184448/2964949001191424/STEM/a728d45c-04c3-4649-bd1f-1353a526477c.png?resizew=135)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966903d099ea0534ab7019d9346f89c4.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37793a3a810e823e10c340986f55ddd.png)
您最近一年使用:0次
9 . 如图,在正四棱柱
中,底面
边长为1,侧棱
,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/2022/4/22/2963685459812352/2964935615856640/STEM/b1ec2bcc-d4c9-479b-9b00-42c300866c17.png?resizew=160)
(1)求直线
与平面
所成角的大小;(结果用反三角函数值表示)
(2)求直线
与平面
之间的距离.
![](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/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/2022/4/22/2963685459812352/2964935615856640/STEM/b1ec2bcc-d4c9-479b-9b00-42c300866c17.png?resizew=160)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15dc61d5de97b5a40be925b278ae494c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/408871c2b71ef88d6f556ce53cf73cc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
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名校
10 . 如图,正方体
的棱长为1,线段
上有两个动点E,F,且
,则( )
![](https://img.xkw.com/dksih/QBM/2022/4/20/2962428932464640/2963646105591808/STEM/488e3cf3-dad7-40bb-8df2-278f012d627b.png?resizew=186)
![](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/e438a162ed349f7f25333e8f6c044e6d.png)
![](https://img.xkw.com/dksih/QBM/2022/4/20/2962428932464640/2963646105591808/STEM/488e3cf3-dad7-40bb-8df2-278f012d627b.png?resizew=186)
A.![]() | B.![]() |
C.直线AB与平面BEF所成的角为定值 | D.以ABEF为顶点的四面体的体积随EF位置的变化而变化 |
您最近一年使用:0次