1 . 在四棱锥
中,底面
是边长为
的正方形,顶点
在底面内的射影
在正方形
的内部(不在边上),且
,
为常数,设侧面
与底面
所成的二面角依次为
,则下列各式为常数的是( )
①
②
③
④![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b8ce39f25b73f8b2e33e5977881f4b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c108b335ca10bd2a6fd7d90e7287f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2338b97ef987779263cba61ceb790082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68bdeb716a658088cb15f94d07d73409.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fbeee7959e179725a9b251bb269da6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4886dc9ec29d6e974cbbb56689eef40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a702c8b3689f20c9d43641afdf0e4b0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b8ce39f25b73f8b2e33e5977881f4b4.png)
A.①② | B.②④ | C.②③ | D.③④ |
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解题方法
2 . 如图,在正方体
中,E是棱
上的动点,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/9e0f988b-a205-4fe0-b147-f46c6c4e3211.png?resizew=160)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/9e0f988b-a205-4fe0-b147-f46c6c4e3211.png?resizew=160)
A.直线![]() ![]() ![]() |
B.直线![]() ![]() ![]() |
C.二面角![]() |
D.直线![]() ![]() |
您最近一年使用:0次
名校
解题方法
3 . 在
中,
,将
沿
翻折,使
,则平面
与平面
夹角的余弦值是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/15/3545edd1-d50b-4ff7-86ce-76b4b0ad7f9d.png?resizew=176)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5138a9f70d5e8b0580e30fef6eb7baef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dae7ef987d936f54c5396b5c5a05a0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af633abfe3cb03f1836db6c570a5bcc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb49d869110f27140f5c1934143db2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8010e1a73f05117a278860c1c0c7f147.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/15/3545edd1-d50b-4ff7-86ce-76b4b0ad7f9d.png?resizew=176)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
4 . 在菱形
中,
,将
沿对角线
折起,使点A到达
的位置,且二面角
为直二面角,则三棱锥
的外接球的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84bc097b8f3d690178ce181b5829e174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc66a96c1297e7068e987e0e70723e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb4c6e9a723aa843e6ba62d7c1a3a6c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-12-27更新
|
1280次组卷
|
10卷引用:模块六 立体几何 大招13 外接球之折叠模型
(已下线)模块六 立体几何 大招13 外接球之折叠模型海南省海口市海口中学2024届高三上学期第四次月考数学试题江西省赣州市南康中学2024届高三上学期七省联考考前数学猜题卷(八)广东省广州市广雅中学2024届高三上学期第二次调研数学试题(已下线)专题05 空间向量与立体几何(分层练)(四大题型+21道精选真题)(已下线)黄金卷07(2024新题型)(已下线)第二章 立体几何中的计算 专题六 几何体的外接球、棱切球、内切球 微点10 切瓜模型综合训练【基础版】(已下线)第八章 立体几何初步(压轴题专练)-单元速记·巧练(人教A版2019必修第二册)(已下线)第八章 立体几何初步(一)(知识归纳+题型突破)(2)-单元速记·巧练(人教A版2019必修第二册)(已下线)专题突破:立体几何外接球的常见模型-同步题型分类归纳讲与练(人教A版2019必修第二册)
5 . 如图所示,两个不同的平面
,A、B两点在两平面的交线上,
,以AB为直径的圆
在平面
内,以AB为长轴,F、
为焦点的椭圆
在平面
内.过圆
上一点P向平面
作垂线,垂足为H,已知
,且
.若射线FH与椭圆相交于点Q,且
,在平面
内,以点H为圆心,半径为4的圆经过点Q,且圆H与直线AB相切.则平面
所成的角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55e53935c33d94f4bb102a25f3a24cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d00be47dcb89793f14a2fd10f4c522b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e55590555905eb4f57889bbd16e39a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbdb723f44e216e920395a08f4513ab4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93989989b7c49a508b21d91de733078.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d05b98b47a3eac81bb22afdc3d7a888.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc14778010a33f90902ff17b1ec0ac73.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-12-21更新
|
230次组卷
|
3卷引用:湖北省云学名校联盟2023-2024学年高二上学期12月联考数学试题
6 . 如图,已知
为圆的直径,且
,
垂直于圆所在的平面,且
,
是圆周上一点,
,则二面角
的大小为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/d84bc398-bdb9-4309-8da0-f138c15ab8f6.png?resizew=158)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/491c3a4f72b84ebadd28b90711435adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80be421a052e5eb07a61115d89cdf9ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec2e8d4093704e39fb71b25e1ee5652f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/d84bc398-bdb9-4309-8da0-f138c15ab8f6.png?resizew=158)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
7 . 如图,在三棱锥
中,
平面
,则下列选项中,不正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/e5f95287-5273-4257-81be-2080edaead2f.png?resizew=153)
![](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/db0ce0650b58d8b11b764a5bd67b0fe4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/19/e5f95287-5273-4257-81be-2080edaead2f.png?resizew=153)
A.平面![]() ![]() |
B.二面角![]() ![]() |
C.![]() ![]() ![]() |
D.三棱锥![]() ![]() |
您最近一年使用:0次
名校
8 . 在三棱锥
中,
,
,
,二面角
的大小为
,则三棱锥
外接球的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55ca6072b3a2aac406a2b60bb7e01cde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10be1272ae0edd88131f0db7d1518eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76dde16b05fba6fc61779511e63f34fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-12-12更新
|
782次组卷
|
5卷引用:浙江省强基联盟2023-2024学年高二上学期12月联考数学试卷
浙江省强基联盟2023-2024学年高二上学期12月联考数学试卷广东省广州市广东实验中学2024届高三上学期大湾区数学冲刺卷(四)(已下线)重难点6-3 立体几何外接球与内切球问题(12题型+满分技巧+限时检测)(已下线)第二章 立体几何中的计算 专题六 几何体的外接球、棱切球、内切球 微点12 二面角的四面体模型综合训练【基础版】(已下线)第八章 立体几何初步(一)(知识归纳+题型突破)(2)-单元速记·巧练(人教A版2019必修第二册)
解题方法
9 . 在边长为
的等边三角形
中,
于
,沿
折成二面角
后,
,此时二面角
的大小为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f215a42c4b7078d8d65923eb9980e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd29cc627d76412c236aac6b29fa0fdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b484a5f91810a552a4aa9c8a534d7a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd29cc627d76412c236aac6b29fa0fdf.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
解题方法
10 . 正方体
中,
是
的中点,
是线段
上的一点.给出下列命题:
①平面
中一定存在直线与平面
垂直
②平面
中一定存在直线与平面
平行
③平面
与平面
所成的锐二面角不小于![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
④当点
从点
移动到点
时,点
到平面
的距离逐渐增大
其中正确命题的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e935bb9d7b7115429edbd1e7469af65.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/16/0cc80a7f-880f-4ba7-827b-b86d3243bff5.png?resizew=159)
①平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df5935c893580c77ab6fa6eb0a70bdb.png)
②平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df5935c893580c77ab6fa6eb0a70bdb.png)
③平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df5935c893580c77ab6fa6eb0a70bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
④当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df5935c893580c77ab6fa6eb0a70bdb.png)
其中正确命题的序号是( )
A.②③ | B.①③ | C.①④ | D.②④ |
您最近一年使用:0次