1 . 如图,在平行四边形
中,
,且
交
于点
,现沿折痕
将
折起,直至满足条件
,此时![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8236c5bea602a5e97d2f93472474770.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05c1d9c9309897e129405f3bd7c858e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ac5396c5ea442e0364b50c1db3d2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51b89f545616ef48f3706850107ad95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8236c5bea602a5e97d2f93472474770.png)
您最近一年使用:0次
2024-03-14更新
|
274次组卷
|
4卷引用:四川省成都市成华区某校2023-2024学年高三下学期“三诊”数学(理)试题
名校
解题方法
2 . 将正方形
沿对角线
折起,当
时,三棱锥
的体积为
,则该三棱锥外接球的体积为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1f4f255d191786f7d330d278868c2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f83dbfddc6f98548699ed581e8c8608.png)
您最近一年使用:0次
2024-01-18更新
|
1360次组卷
|
4卷引用:四川省绵阳南山中学2024届高三下学期4月绵阳三诊热身考试理科数学试题
3 . 如图,已知在棱长为2的正方体
中,点E,F,H分别是
,
,
的中点,点G是
上的动点,下列结论中正确的有________________ .
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/cf1e3d64-9f44-4305-9b4d-4d194ea209e0.png?resizew=138)
①
平面ABH ②
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/319ad7c7bdb5c5cfa477eb4f5ea57d2b.png)
③直线EF与
所成的角为
④三棱锥
的体积最大值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/30/cf1e3d64-9f44-4305-9b4d-4d194ea209e0.png?resizew=138)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cae8fd28341fc24851e03e9ba1d4e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d1d2e0f281222a5f289ea4008370aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/319ad7c7bdb5c5cfa477eb4f5ea57d2b.png)
③直线EF与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/996bf3d35b6763cbc1a423b13a9df2dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50c9299f4c44108e7808d6270fe6f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a391005600bdd69c96750589f9adb048.png)
您最近一年使用:0次
解题方法
4 . 已知四棱锥
的底面是边长为2的正方形,
,二面角
的余弦值为
,则四棱锥
的外接球的表面积为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2d61774ad99cc43045644d18f1c5ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02a7ba7cd0c654714c967a900513ba16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35ca4419cbe7c3dc2e40d0a17c9cad24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
名校
解题方法
5 . 在梯形
中,
,
,
,将
沿
折起,连接
,得到三棱锥
,当三棱锥
的体积取得最大值时,该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/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f841c80511eeb80156d2eba7932851c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.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/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
您最近一年使用:0次
2023-09-10更新
|
874次组卷
|
9卷引用:四川省成都市石室天府中学2024届高三一诊模拟考试二数学(理)试题
四川省成都市石室天府中学2024届高三一诊模拟考试二数学(理)试题四川省南充市阆中市阆中中学校2023-2024学年高二上学期11月月考数学试题湖北省孝感市部分学校2023-2024学年高二上学期9月起点考试数学试题广东省汕尾市华大实验学校2023-2024学年高二上学期9月月考数学试题湖北省武汉市第四中学2023-2024学年高二上学期10月月考数学试题湖南省邵阳市邵东市第一中学2023-2024学年高二上学期12月月考数学试题(已下线)第11章 简单几何体(压轴必刷30题专项训练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(沪教版2020必修第三册)湖南省衡阳市第八中学2023-2024学年高二上学期期末考试数学试题(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13 多边形折叠成二面角模型【基础版】
6 . 如图1,在矩形ABCD中,
,E为AB的中点,将
沿DE折起,点A折起后的位置记为点
,得到四棱锥
,M为
的中点,如图2.某同学在探究翻折过程中线面位置关系时,得到下列四个结论:
;
②异面直线
所成角的正切值为2;
③存在某个位置,使得 平面
平面
.
④三棱锥
的体积的最大值为
;
其中所有正确结论的序号是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80f51c31583fea58fde645474d60b8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db2b1c641b93caae9b7a82441e4ba70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/371e9c541c4eeecf91967ceb24d77c9c.png)
②异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d27f63a4a2e058b302674c086d5085.png)
③存在某个位置,使得 平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b3e7c7845a0ec3cbac709fda131764.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74bca84ad86c648d3bb20c8909c8da3f.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53d5cf6415cc66f3617f330f28ae09fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11b9f96b8ecc3cb000bb2f030809f225.png)
其中所有正确结论的序号是
您最近一年使用:0次
2023-09-06更新
|
471次组卷
|
3卷引用:四川省叙永第一中学校2024届高三上学期一诊数学(理科)试题
7 . 在四棱锥
中,
,
,
,
,则三棱锥
外接球的表面积为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d798b1265585876e87287ef3d69ce596.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d89b3c307146c539b2e620d30869cf8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500e390f6d083b96a4685a37f4c68b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d535bfd65eb04a29d64425d54b2acf86.png)
您最近一年使用:0次
名校
8 . 已知A,B两点都在以PC为直径的球O的表面上,
,
,
,若球
的体积为
,则异面直线
与
所成角的余弦值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c47eb6743075d149f8dc688aca72a00a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
您最近一年使用:0次
2023-08-09更新
|
743次组卷
|
9卷引用:四川省成都市第七中学2023届高考模拟文科数学试题
解题方法
9 . 表面积为
的球面上有四点S、A、B、C,△ABC是等边三角形,球心O到平面ABC的距离为2,若面SAB⊥面ABC,则棱锥
体积的最大值为___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c1a84932df6ed29a15050c61a37fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/24/8a19ff9f-4b2a-401d-83fa-8de5039e5715.png?resizew=157)
您最近一年使用:0次
名校
10 . 如图,AB为圆柱下底面圆O的直径,C是下底面圆周上一点,已知
,
,圆柱的高为5.若点D在圆柱表面上运动,且满足
,则点D的轨迹所围成图形的面积为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3925e45d83a5383e492cdb1666493cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9774f83067ed956a551bc41adcce0469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6acb01ba645b38cb536570e5fd7318f7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/11/b60ae1e1-b1e6-4f77-93e1-1c9e40ea0a1c.png?resizew=108)
您最近一年使用:0次
2023-05-10更新
|
973次组卷
|
7卷引用:四川省成都市2023届高三三诊文科数学试题
四川省成都市2023届高三三诊文科数学试题四川省凉山州宁南中学2022-2023学年高二下学期第二次月考文科数学试题四川省凉山州宁南中学2022-2023学年高二下学期第二次月考理科数学试题(已下线)第02讲 1.1.2空间向量的数量积运算(7类热点题型讲练)-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第一册)(已下线)阶段性检测3.2(中)(范围:集合至立体几何)(已下线)重难点突破04 立体几何中的轨迹问题(六大题型)(已下线)第三章 空间轨迹问题 专题五 微点1 翻折、旋转问题中的轨迹问题【培优版】