1 . 如图,在四棱柱
中,四边形
为菱形,四边形
为矩形,
,
,
,二面角
的大小为
,
分别为BC,
的中点.
(1)求证:
;
(2)求直线
与平面BCN所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffc2817fa590affb5a760a25dc65308.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131c735c1736250c608af9f0d2d185fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9977da109ae8644f94b286ccded8cc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/14/c1a3264e-317e-4b6e-89d0-be06cab5285c.png?resizew=193)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/598dc6b5a7737df67f6df097da7866b0.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
您最近一年使用:0次
2 . 在一次立体几何模型的实践课上,老师要求学生将边长为4的正方形ABCD沿对角线AC进行翻折,使得D到达
的位置,此时平面
平面
,连接
,得到四面体
,记四面体
的外接球球心为O,则点O到平面
的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/feb3c5eea67eecdd13a2e6cd60d1d67e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb49d869110f27140f5c1934143db2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b435d7fc33860ae191f9111d880b40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591827e255a9a80766da16e29beb94c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/591827e255a9a80766da16e29beb94c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae9bd3db15b3c5062240b4438fe6476.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
3 . 如图1,在梯形
中,
,过
分别作梯形的高
,交
于点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c739074553618fbb8d242ca53976384.png)
,沿
所在直线将梯形折叠,使得点
与点
重合,记为点
,如图2,M是
中点,
是
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/27/5214425d-ec5b-4e0a-821b-ddf877a78e21.png?resizew=355)
(1)证明:直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
平面
;
(2)
是线段
上异于端点的一点,从条件①、条件②、条件③中选择一个作为已知,求平面
与平面
的夹角的余弦值.
条件①:
;
条件②:四棱锥
的体积为
;
条件③:点
到平面
的距离为
;
注:如果选择多个条件分别解答,按第一个解答计分.
![](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/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925b8db9b6ed790adf04a5dff4e0e61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c739074553618fbb8d242ca53976384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40be06d1ee73fd02f0a6039081dc4c5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925b8db9b6ed790adf04a5dff4e0e61a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/27/5214425d-ec5b-4e0a-821b-ddf877a78e21.png?resizew=355)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4739ad948445af72d585fe29c745929b.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/149596fee6ed1e2d19fd8dadc14a8baf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c5a4dfcf4c24a8ecb210cc4c53db221.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74d761129d39626d79053680475caba8.png)
条件②:四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/504c7cd04dc84c872e5539d9906bd36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
条件③:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d246f9eceab371ebf47a47c2f11a4ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
注:如果选择多个条件分别解答,按第一个解答计分.
您最近一年使用:0次
4 . 《几何原本》是古希腊数学家欧几里得的数学著作,其中第十一卷称轴截面为等腰直角三角形的圆锥为直角圆锥.已知圆锥
是直角圆锥,底面直径
是圆锥侧面上一点,若点
到圆锥底面的距离为1,则三棱锥
体积的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f74c3b0f7dead2845b967c419404d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bffd3b6cf2e17d221c8aaeb70e81ef48.png)
您最近一年使用:0次
解题方法
5 . 如图,在直三棱柱
中,
,
分别为
的中点.
(1)求证:
CM;
(2)求证:
平面
;
(3)设
为
上一点,且
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986ba572d8373df48c996f8c8611498c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8ae465bd880e7e2eda6fb28b2167d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/566ab6b669159a99d683bcfe535f96c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c14dd6a3395dfbf4814fd4ea2570ad5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/19/917373dd-3c6b-40b8-99ab-b54a1a2f828d.png?resizew=152)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c7c261740ac2ae26715e1298ca278a2.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c7c261740ac2ae26715e1298ca278a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f491a794b9ac1a85a18c87ecee616c.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53da1233648a05263daed8dfd371447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f491a794b9ac1a85a18c87ecee616c.png)
您最近一年使用:0次
名校
6 . 如图所示,四棱锥
中,平面
平面
,底面
是边长为2正方形,
,
与
交于点
,点
在线段
上.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/15/0b623d04-c3f5-4aa5-ada2-6c84ee345504.png?resizew=179)
(1)求证:
平面
;
(2)若
平面
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877582b5387278008d14fe5932622fe7.png)
![](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/c45a82d9488f12d638f56b98d4053117.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defa5b53043ae802bb1af7d14374406d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/15/0b623d04-c3f5-4aa5-ada2-6c84ee345504.png?resizew=179)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3a04ea8ebc597fd1f5d6bb8df181a2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc9c9cfa597b444b5c9dbae7a825a695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc6f6dfdbe7d39891c35f67e1a95c7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca48c18021e7be4bbb3e95576e1c1b5f.png)
您最近一年使用:0次
2023-04-14更新
|
1097次组卷
|
5卷引用:海南省海口市秀英区海口嘉勋高级中学2024届高三上学期开学考试数学试题
海南省海口市秀英区海口嘉勋高级中学2024届高三上学期开学考试数学试题海南省海口观澜湖华侨学校2023届高三第六次考试数学试题(已下线)湖南省新高考教学教研联盟2023届高三下学期4月第二次联考数学试题变式题17-22(已下线)专题10 立体几何综合-2湖南省张家界市慈利县第一中学2022-2023学年高二下学期期中数学试题
9-10高二下·浙江宁波·期末
名校
解题方法
7 . 已知四棱锥
的底面为直角梯形,
,
底面
,且
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2021/8/5/2779732172177408/2781131262238720/STEM/f87754a6ddc44602b1b7af31bf921983.png?resizew=186)
(1)求
与
所成角的余弦值;
(2)求面
与面
所成夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd8e727e4efc22b49649f71ae9c9d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73196f5c58487dd02521aa39ffe5fe50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc5c73fb6bd925b344b66ac4325e81aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/2021/8/5/2779732172177408/2781131262238720/STEM/f87754a6ddc44602b1b7af31bf921983.png?resizew=186)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(2)求面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53bdef2e7a7929ad6190302ab44c46c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17c5ef850e256c98ca4f033999e61311.png)
您最近一年使用:0次
2021-08-07更新
|
330次组卷
|
6卷引用:海南省三亚华侨学校南新校区2023届高三上学期开学摸底考试数学试题
海南省三亚华侨学校南新校区2023届高三上学期开学摸底考试数学试题(已下线)2011届江苏省盐城市高三摸底考试数学卷江苏省淮安市淮阴中学2019-2020学年高三上学期11月联考数学试题吉林省长春外国语学校2021-2022学年高二下学期期初考试数学试题(已下线)2010年浙江省宁波市八校联考高二第二学期期末数学(理)试题新疆乌鲁木齐市第八中学2018-2019学年高二上学期期中考试数学试题
名校
解题方法
8 . 某几何体的三视图如图所示,则该几何体的表面积为
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/2c4bb437-e309-4a68-8707-02e158d938d1.png?resizew=208)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/2c4bb437-e309-4a68-8707-02e158d938d1.png?resizew=208)
A.46 | B.48 | C.50 | D.52 |
您最近一年使用:0次
2019-06-19更新
|
953次组卷
|
18卷引用:海南省(海南中学、文昌中学、海口市第一中学、农垦中学)等八校2018届高三上学期新起点联盟考试数学(文)试题
海南省(海南中学、文昌中学、海口市第一中学、农垦中学)等八校2018届高三上学期新起点联盟考试数学(文)试题海南省(海南中学、文昌中学、海口市第一中学、农垦中学)等八校2018届高三上学期新起点联盟考试数学(理)试题辽宁省葫芦岛第六高级中学2017-2018学年高三上学期第二次阶段(期中)考试题数学(文)辽宁省葫芦岛第六高级中学2017-2018学年高三上学期第二次阶段(期中)考试题数学(理)(已下线)2019年4月18日《每日一题》理数三轮复习- 空间几何体的三视图、表面积和体积(已下线)2019年4月18日 《每日一题》文数三轮复习-空间几何体的三视图、表面积和体积河北省正定中学2016-2017学年高二下学期第四次月考(期末)数学(理)试题河北省正定中学2016-2017学年高二下学期第四次月考(期末)数学(文)试题河南省平顶山市、许昌市、汝州2017-2018学年高一上学期第三次联考数学试题辽宁省葫芦岛市六校协作体2017-2018学年高一12月月考数学试题(已下线)黄金30题系列 高一年级数学(必修一+必修二) 小题好拿分【提升版】广西南宁市第三中学中学2017-2018学年高二上学期第三次月考数学(文)试题广西陆川中学2017-2018学年高一上学期期末考试数学试题(已下线)2019年6月5日 《每日一题》文数-三视图云南省曲靖市会泽县茚旺高级中学2018-2019学年高二下学期期中考试数学(文)试题云南省曲靖市会泽县茚旺高级中学2018-2019学年高二下学期期中考试数学(理)试题宁夏石嘴山市第三中学2017-2018学年高一(创新班)上学期期末数学试题新疆克拉玛依市第一中学2018-2019学年高一下学期期末数学试题
9 . 如图,已知四棱锥中,四边形
为矩形,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/232db910-484b-4f74-a430-b701d14757ae.png?resizew=195)
(1)求证:
平面
;
(2)设
,求平面
与平面
所成的二面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da426f62147ca7fb8d3314ca9dffbeb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9971233dc3e8ef828046fbb94101b9d0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/232db910-484b-4f74-a430-b701d14757ae.png?resizew=195)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6deecf9ccb7b7879455050633219e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d923a338dd2d2e29336b42574d38448.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ba64da45f618432d6d76b962a41520d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73f7e6fc8324f9f7f826677be25a6479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21665d21bbfb04410c78345de1fd15ae.png)
您最近一年使用:0次
2019-05-12更新
|
756次组卷
|
3卷引用:海南省三亚华侨学校2020届高三下学期开学测试数学试题
名校
解题方法
10 . 如图,三棱柱
的所有棱长均为2,平面
平面
,
,
为
的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/23/046e619b-8699-4871-a9cf-56600963ee6d.png?resizew=228)
(1)证明:
平面
;
(2)若
是棱
的中点,求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131c735c1736250c608af9f0d2d185fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5adb94abf5e78c3bf7d9bced713017a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/23/046e619b-8699-4871-a9cf-56600963ee6d.png?resizew=228)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4560fa4ad459b58b723c74bd24e51ebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e7bf264e78726dd716534bcfc117b1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ac0aa6359834f08349fa6b3ab35c289.png)
您最近一年使用:0次
2017-09-02更新
|
475次组卷
|
3卷引用:海南省(海南中学、文昌中学、海口市第一中学、农垦中学)等八校2018届高三上学期新起点联盟考试数学(文)试题