名校
1 . 在四棱锥
中,底面
是正方形,
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/5/7/2715986552438784/2794686000177152/STEM/68e72234-67af-44f7-8d52-b7aa81a8a350.png?resizew=177)
(1)分别取侧棱
、
中点
、
,证明:直线
与平面
平行;
(2)求四棱锥
的表面积.
![](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/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://img.xkw.com/dksih/QBM/2021/5/7/2715986552438784/2794686000177152/STEM/68e72234-67af-44f7-8d52-b7aa81a8a350.png?resizew=177)
(1)分别取侧棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.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/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
2021-08-26更新
|
250次组卷
|
4卷引用:上海市建平中学2020-2021学年高二下学期期中数学试题
上海市建平中学2020-2021学年高二下学期期中数学试题江西省遂川中学2021-2022学年高二上学期第二次月考数学(理)试题(B卷)上海市徐汇中学2022-2023学年高二上学期期中数学试题(已下线)第04讲线线、线面、面面平行的判定与性质(核心考点讲与练)(3)
名校
解题方法
2 . 已知完全封闭且内部中空的圆柱底面的半径为
,母线长为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/a203b5e8-b79f-497d-ac65-8813b68e26c6.png?resizew=217)
(1)当
,
时,在圆柱内放一个半径为1的实心球,求圆柱内空余部分的体积;(结果用精确值表示)
(2)如图,当
,
时,平面
与圆柱
底面所成锐二面角为45°,且平面
只与圆柱
侧面相交,设平面
与圆柱
侧面相交的轨迹为曲线
,半径为1的两个球分别在圆柱内平面
上下两侧且分别与平面
相切于点
、
,若以点
、
所在直线为
轴,线段
的中垂线为
轴建立平面直角坐标系,求证:曲线
是椭圆并写出椭圆标准方程;
(3)在(1)的条件下,在圆柱内部空余的地方放入和实心球、侧面及相应底面均相切的半径为
的同样大小的小球
个,当
取得最大值
时,求
的值.(结果用数字表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/a203b5e8-b79f-497d-ac65-8813b68e26c6.png?resizew=217)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c572083c2af625b8222e19a53a5d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61318c3e8dd2eda4f1d95094c9a2b301.png)
(2)如图,当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c572083c2af625b8222e19a53a5d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72dab760e63b18eb9162907a11614d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)在(1)的条件下,在圆柱内部空余的地方放入和实心球、侧面及相应底面均相切的半径为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c1936889914a33dfe984171144305.png)
您最近一年使用:0次
名校
3 . 已知地球的半径为R,在北纬60°圈上有A、B两点.若点A的经度为东经65°,点B的经度为西经55°,求A、B两点的球面距离.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/6366632d-0458-4c00-99cf-158027be2f10.png?resizew=195)
您最近一年使用:0次
4 . 如图,在直三棱柱
中,AC=BC=2,
,∠ACB=90°,E,F分别为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/711bd603-158b-436e-9437-efd43d426636.png?resizew=139)
(1)求异面直线
与EF所成角的大小;
(2)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8cb98c0adee7ca698d8b17dacb845b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebaa1096d25a7230290e188aad966b50.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/711bd603-158b-436e-9437-efd43d426636.png?resizew=139)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfcd4aa8e2e84c4605a84097167e216a.png)
您最近一年使用:0次
5 . 如图,在正四棱柱
中,
,
,M为棱
的中点
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/a9888988-b90e-4111-945b-4dadfff6b41b.png?resizew=125)
(1)求三棱锥
的体积;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8cb98c0adee7ca698d8b17dacb845b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/a9888988-b90e-4111-945b-4dadfff6b41b.png?resizew=125)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/283f3b88373640e012bbcd78931d1065.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5563473602e1b17d582a165b7b7b6b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
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解题方法
6 . 如图,正四棱柱
的底面边长为1,异面直线AD与BC1所成角的大小为60°,求A1B1到底面ABCD的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
您最近一年使用:0次
2021-08-09更新
|
1018次组卷
|
8卷引用:上海市静安区2020-2021学年高二下学期期末数学试题
上海市静安区2020-2021学年高二下学期期末数学试题(已下线)第06讲 点面、线面、面面、异面直线的距离(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)专题05异面直线间的距离(1个知识点4种题型1种高考考法)-【倍速学习法】2023-2024学年高二数学核心知识点与常见题型通关讲解练(沪教版2020必修第三册)(已下线)第27讲 空间点、直线、平面之间的位置关系2(已下线)模块三 专题7 大题分类练(立体几何初步)基础夯实练(人教A)(已下线)模块三 专题8(立体几何初步)基础夯实练(北师大版)(已下线)模块三 专题8 大题分类练(立体几何初步)基础夯实练(苏教版)(已下线)重难点专题15 空间中的五种距离问题-【帮课堂】(苏教版2019必修第二册)
7 . 已知如图①,在菱形ABCD中,
且
,
为AD的中点,将
沿BE折起使
,得到如图②所示的四棱锥
,在四棱锥
中,求解下列问题:
![](https://img.xkw.com/dksih/QBM/2021/6/21/2747941734260736/2782024334655488/STEM/7ffd700db791441cbc22fa2a1c5e3bae.png?resizew=394)
(1)求证:BC
平面ABE;
(2)求直线BC与平面ABD所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cdf6426f0eaa95c31648895d35fe165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a88c44f558705de3bcefcfc0ece96b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
![](https://img.xkw.com/dksih/QBM/2021/6/21/2747941734260736/2782024334655488/STEM/7ffd700db791441cbc22fa2a1c5e3bae.png?resizew=394)
(1)求证:BC
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
(2)求直线BC与平面ABD所成角的大小.
您最近一年使用:0次
名校
8 . 中国古代数学名著《九章算术》中记载:“刍(chú)甍(méng)者,下有袤有广,而上有袤无广.刍,草也.甍,屋盖也.”翻译为“底面有长有宽为矩形,顶部只有长没有宽为一条楼.刍字面意思为茅草屋顶.”现有一个刍如图所示,四边形
为正方形,四边形
,
为两个全等的等腰梯形,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/238e84b4-88c0-4282-a641-a67cc1a965d4.png?resizew=181)
(1)求二面角
的大小;
(2)求三棱锥
的体积;
(3)点
在直线
上,满足
(
),在直线
上是否存在点
,使
平面
?若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369eb8ad56da7dc1cdb7c43762be4bee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e41d3f7d55fcbaebc4e2450ac63a3dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed6034301fc4110da89bdb0f46ad82ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/510b162030e04fab26e05fe268675c07.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/238e84b4-88c0-4282-a641-a67cc1a965d4.png?resizew=181)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a34e44c5d7e1d22521fb293994f5b0.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b635e62c3b1f4a57feac8d22be84ee.png)
(3)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/885f6c143bd3b2f9860d94b969b3c5da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe9e329f2730b2be926b121f1ae04c0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a46435220a682a6f67d7ac8608be1c7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc46688d8723cf2003fc25890265200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7081090993015b5058f60ca45af968ae.png)
您最近一年使用:0次
2021-08-02更新
|
853次组卷
|
8卷引用:上海市控江中学2021-2022学年高二上学期期中数学试题
上海市控江中学2021-2022学年高二上学期期中数学试题山东省济南市2020-2021学年高一下学期期末数学试题(已下线)专题02 立体几何中存在性问题的向量解法-【重难点突破】2021-2022学年高二数学上册常考题专练(人教A版2019选择性必修第一册)上海市市西中学2022-2023学年高二上学期期中数学试题(已下线)第04讲线线、线面、面面平行的判定与性质(核心考点讲与练)(3)上海市文来高中2022-2023学年高一上学期期中数学试题(已下线)高一下学期期末真题精选(压轴60题20个考点专练)-【满分全攻略】2022-2023学年高一数学下学期核心考点+重难点讲练与测试(人教A版2019必修第二册)(已下线)第一章 空间向量与立体几何(压轴必刷30题4种题型专项训练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)
名校
解题方法
9 . 如图,在四棱锥
中,底面
是菱形,
平面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/6/29/2753632147513344/2767720843534336/STEM/e02e3f5b4b9c403aa5d815be1dc016f6.png?resizew=178)
(1)若
,E为
的中点,求异面直线
与
所成角的大小;
(2)若
,求二面角
的大小;
(3)试求四棱锥
的体积
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb4564baf209de77802d46cda82995c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a9fa8832f98b5418a7d75892f7951b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3bf906a702ee1ede7aeadc9c93d54d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60bd1467044c0295b25b554248769186.png)
![](https://img.xkw.com/dksih/QBM/2021/6/29/2753632147513344/2767720843534336/STEM/e02e3f5b4b9c403aa5d815be1dc016f6.png?resizew=178)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f88e011f6694ca0c9634ee5cdfce443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d260c4df7b0dc180af6980d21f3371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e61620a272dada8d4b9a9fab6379dfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0213c5787a5a6b38d11bceca5567f67.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f88e011f6694ca0c9634ee5cdfce443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffbd0347827bd713b484ba20dffe0a40.png)
(3)试求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
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5卷引用:上海市实验学校2020-2021学年高二下学期期末数学试题
上海市实验学校2020-2021学年高二下学期期末数学试题上海市松江二中2021-2022学年高二上学期期中数学试题上海市上海师范大学附属外国语中学2021-2022学年高二上学期12月月考数学试题(已下线)专题04 空间向量与立体几何的压轴题(二)-【尖子生专用】2021-2022学年高二数学考点培优训练(人教A版2019选择性必修第一册)(已下线)第04讲 空间向量的应用(教师版)-【帮课堂】
名校
解题方法
10 . 如图,圆锥的顶点是
,底面中心为
,
是与底面直径
垂直的一条半径,
是母线
的中点.
![](https://img.xkw.com/dksih/QBM/2021/7/6/2758529858240512/2766958380466176/STEM/7631fe1b-d11d-497f-b7a3-eb5eaa15e11f.png?resizew=221)
(1)设圆锥的高为
,异面直线
与
所成角为
,求圆锥的体积;
(2)当圆锥的高和底面半径是(1)中的值时,求直线
与平面
的所成角大小.
![](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/828628c0876b45381c9a0edeb0fec236.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/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://img.xkw.com/dksih/QBM/2021/7/6/2758529858240512/2766958380466176/STEM/7631fe1b-d11d-497f-b7a3-eb5eaa15e11f.png?resizew=221)
(1)设圆锥的高为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e32a929349d630f8086fd4111a9d84ee.png)
(2)当圆锥的高和底面半径是(1)中的值时,求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
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2卷引用:上海市大同中学2020-2021学年高二下学期期末数学试题