名校
1 . 如图,在多面体
中,平面
平面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/16/ee55d280-2694-4a53-9b85-dc10cb93c16c.png?resizew=200)
(1)求证:
;
(2)若四边形
为矩形,且
,求直线
与平面
所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2a4e3f0349fa83dc2a0b7d798f04843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/829018a6ca0aff95d89e3f7cd943274e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/16/ee55d280-2694-4a53-9b85-dc10cb93c16c.png?resizew=200)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70c5fd65265f85df7d149d83d80d4e62.png)
(2)若四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4b93d7abcfc4c3df48f03aa969c17f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/755b680b34589e9caa1920bf5a8d3258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422210c777ac0d625bbd81cc7601bf9b.png)
您最近一年使用:0次
解题方法
2 . 如图,在正四棱柱
中,
,
,点
在棱
上,且
,点
在上底面
运动,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb514bc9eeabe59f4f585aebf50f2443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/26/e3103078-c3fd-4852-8361-21c5a70dbf20.png?resizew=147)
A.存在点![]() ![]() |
B.不存在点![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-05-26更新
|
1075次组卷
|
3卷引用:专题14 立体几何小题综合
2023高三·全国·专题练习
名校
解题方法
3 . 如图,在矩形
中,
,沿
将
折起,当三棱锥
的体积取得最大值时,
与平面
所成角的正切值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b124087e8e0f003f15224ecc3c983228.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c41ffdaecfb3c73d403179e5745c71a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
您最近一年使用:0次
2023-05-22更新
|
991次组卷
|
3卷引用:天津市耀华中学2023-2024学年高一下学期学科训练(二)数学试卷
名校
4 . 如图,在矩形
中,
,
,E为AD的中点,将
沿
翻折成
,记二面角
的平面角为θ,在翻折过程中,下列结论成立的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f144992e1cbee34868abce1e5ad38c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438bf2134641f9950932bd667188d63c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8267d832508d4bee00ff2d4a4bd2b6e5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/13/22d038a6-0d85-4215-97b0-0599141ae01d.png?resizew=312)
A.点![]() ![]() |
B.存在点![]() ![]() |
C.![]() |
D.记![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
5 . 如图所示,直角梯形
和三角形
所在平面互相垂直,
,
,
,
,异面直线
与
所成角为45°.
(1)求证:平面
平面
;
(2)若点
在
上,当
面积最小时,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e223e3b657fe3f5856303f80a276fa0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a338aeca50edcba2a34d9472f3b9844.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1c4c2f7b1b8987384e5c9ea1075750d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/22/a45b4b64-06e0-4b72-9bcd-d6757fd0fe98.png?resizew=130)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc6db50a9709c3f4d84eee7bdf1250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4139b091e9dc432b267ff68420c77de4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3daec02423dbc4bf84b8ec462d12b683.png)
您最近一年使用:0次
2023-05-20更新
|
666次组卷
|
3卷引用:第4讲:立体几何中的最值问题【练】(清北二轮)
名校
解题方法
6 . 如图,直三棱柱
中,
,棱柱的侧棱足够长,点P在棱
上,点
在
上,且
,则当△
的面积取最小值时,三棱锥
的外接球的体积为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f2185273bf04c11118c7954f7ec822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecfa65ef29ceaf783488b0f7ca0d1f45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ecac2dad4cffdd971fd23deacff3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da9942034e527ce669189b973a2fadc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f06ed3e88f623ed9313d06b1bb2a87ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/14/3c44d9b8-4692-4082-8b01-cd4b9a7c3dc1.png?resizew=127)
您最近一年使用:0次
2023-05-12更新
|
1151次组卷
|
5卷引用:辽宁省鞍山市2024届高三上学期期末联考模拟练习数学试题
辽宁省鞍山市2024届高三上学期期末联考模拟练习数学试题山西省名校联盟2023届高三5月仿真模拟数学试题江西省抚州市金溪县2023届高三高考仿真模拟考试数学(文)试题江西省抚州市金溪县2023届高三高考仿真模拟考试数学(理)试题(已下线)重难点突破01 玩转外接球、内切球、棱切球(二十三大题型)-3
名校
解题方法
7 . 如图,球
的表面积为
,四面体
内接于球
,
是边长为
的正三角形,平面
平面
,则该四面体体积的最大值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/12/f1e7bc27-d109-49f1-8ba1-81f2f1ddfc5c.png?resizew=170)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f13e7a0ac71deb6ebb52a637fa07af61.png)
![](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/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/12/f1e7bc27-d109-49f1-8ba1-81f2f1ddfc5c.png?resizew=170)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-05-12更新
|
1096次组卷
|
5卷引用:专题15 球体外接内切综合问题小题
(已下线)专题15 球体外接内切综合问题小题(已下线)题型19 10类球体的外接及内切解题技巧安徽省黄山市2023届高三三模数学试题广东省佛山市南海区华南师范大学附属中学南海实验高级中学2023届高三保温考数学试题(已下线)第七章 综合测试B(提升卷)
解题方法
8 . 已知正方形ABCD所在平面与正方形CDEF所在平面互相垂直,且
,P是对角线CE的中点,Q是对角线BD上一个动点,则P,Q两点之间距离的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
A.1 | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-05-05更新
|
1142次组卷
|
3卷引用:第15讲 8.6.3平面与平面垂直(第2课时)-【帮课堂】(人教A版2019必修第二册)
名校
9 . 如图,在多面体
中,侧面
为菱形,侧面
为直角梯形,
分别为
的中点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/2/480c125d-07de-431c-a71b-413c35489d72.png?resizew=166)
(1)证明:
平面
;
(2)若平面
平面
,多面体
的体积为
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cf2fa3cb87267ee5f968c2a9362d216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9d54cbbf601f4583659771eb534997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0332df44007ede3a48a4cb3c45dfa0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5eedee49f410d11fe03eb5389422d022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92fbe0488899724e45ceb006d055b87d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/2/480c125d-07de-431c-a71b-413c35489d72.png?resizew=166)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9d54cbbf601f4583659771eb534997.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0f23a9fcac0e87e4175cd6131b15ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9d54cbbf601f4583659771eb534997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/149bc19ed62219813a1738616f65c2fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20af148464904e21f4374cc8fb886fba.png)
您最近一年使用:0次
2023-04-28更新
|
1694次组卷
|
5卷引用:江西省吉安市峡江中学2023-2024学年高二上学期期末数学试卷(九省联考题型)
江西省吉安市峡江中学2023-2024学年高二上学期期末数学试卷(九省联考题型)江西省赣抚吉十一校联盟体2023届高三下学期4月联考数学(理)试题江苏省扬州中学2022-2023学年高二下学期5月月考数学试题河南省新乡市第一中学2023届高三三轮冲刺第十测理科数学试题(已下线)专题03 空间向量求角度与距离10种题型归类-【巅峰课堂】2023-2024学年高二数学上学期期中期末复习讲练测(人教A版2019选择性必修第一册)
解题方法
10 . 已知一个球的表面上有四点
、
、
、
,
,
,
,平面
平面
,则该球的表面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1719410d21e3de1242366ce2965e838c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6906f59d09ce31956d6f5ea2b23fc77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef35540101a8d7331dfe62fd1ab4d674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
您最近一年使用:0次
2023-04-26更新
|
626次组卷
|
4卷引用:广西桂林市临桂区第三中学2024届高三下学期4月月考数学试卷
广西桂林市临桂区第三中学2024届高三下学期4月月考数学试卷河南省名校青桐鸣2023届高三下学期4月联考理科数学试题河南省名校青桐鸣2023届高三下学期4月联考文科数学试题(已下线)四川省巴中市2023届高三“一诊”考试数学(理)试题变式题11-15