名校
解题方法
1 . 如图,在边长为4的正方形
中,点
,
分别在边
,
上(不含端点)且
,将
,
分别沿
,
折起,使
,
两点重合于点
,则下列结论错误的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d96a5d40d0aea9f4398ca4d0fe9b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c771a4feb150ad9cff8d70431c97eb17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13668f033d00acfc366f7e47949c4462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/043a2032-f32b-4c60-ad25-db15a6501bda.png?resizew=255)
A.![]() |
B.当![]() ![]() ![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() ![]() |
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名校
2 . 把
沿三条中位线折叠成四面体
,其中
,
,
,则四面体
的外接球表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6fa901208df1a733779f3a1d7aa0f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25845d466e582eeb2b49bbd4bdc7d824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60544ffa6c33391c5a773fc243241802.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cb54d2b7ba202cedd9cce4b476c8e59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-04-01更新
|
423次组卷
|
2卷引用:河南省信阳市新县高级中学2022届高三下学期第三轮适应性考试(五)数学(理科)试题
3 . 已知三棱锥
中三组相对的棱长分别相等,长度分别为
,
,
,其中![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34c590f48c84fe471d1af522c343c59.png)
,则三棱锥
的外接球的表面积的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fdc2ef8de7a4765a4f8780c1b5c3f32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/703d9e332043adad2cecd70a07093262.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da001dad7941e6c9858637d7b62cec59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34c590f48c84fe471d1af522c343c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7dbc702617c765a573961953cc0901.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-02-26更新
|
140次组卷
|
2卷引用:中原名校2022年高三上学期第四次精英联赛理科数学试题
4 . 已知正三棱柱
的六个顶点均在球
的球面上,
为上底面
的外接圆,若
的面积为
,且侧面
为正方形,则球
的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0385df6c7f8ee7ab503b6ed35933695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0385df6c7f8ee7ab503b6ed35933695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e95a79288fcb7e47fba4410722e2bc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-02-23更新
|
107次组卷
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2卷引用:中原名校2022年高三上学期第一次精英联赛文科数学试题
5 . 在边长为1的菱形
中
,将
沿
折起,使二面角
的平面角等于
,连接
,得到三棱锥
,则此三棱锥
外接球的表面积为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c505c02c59313fe0108392a5bf5127.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1854ba6cc92481d7a616bd2788a47e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
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6 . 已知三棱锥
中,
平面
,若
,
,
,
,则三棱锥
的外接球表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e33a849c6276adc188d414b048665f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8c340f8945083d2993ff28eabfcccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7788830ed1cb3b9c5988f70f43595f2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f122069c8c86838a1d886f61adb82c8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 我国古代数学名著《九章算术》中“开立圆术”曰:置积尺数,以十六乘之,九而一,所得开立方除之,即立圆径.“开立圆术”相当于给出了已知球的体积V,求其直径d的一个近似公式
,人们还用过一些类似的近似公式,根据
判断下列近似公式中最精确的一个是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/920f36811932261ab2f8ba6536391b56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/603c47d2b7bd76b97e45603f95403053.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
8 . 如图,
,线段AC,BD相互垂直平分,在扇形OAB中,OA=1,将扇形OAB和
绕AC所在直线旋转一周所得几何体的表面积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/19/596c1a92-b057-4e05-9286-bb3ef1c0d830.png?resizew=159)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7de966c316db1013defc56372fcf814e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4807ca16360c0cca436e59d4be98f626.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/19/596c1a92-b057-4e05-9286-bb3ef1c0d830.png?resizew=159)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-04-16更新
|
243次组卷
|
5卷引用:河南省名校联盟2021-2022学年高一下学期中考试数学试卷
名校
9 . 已知等腰直角
的三个顶点在球O的表面上,且
,连接CO并延长交球O的表面于点D,连接DA,DB;若球O的体积为288π,则直线AC,BD所成角的正切值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4184d0d1b8b79f6f268b7c86e7fda1.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2022-11-26更新
|
656次组卷
|
3卷引用:河南省南阳市第二完全学校高级中学2022-2023学年高三上学期12月月考数学试题
名校
解题方法
10 . 已知三棱柱
的6个顶点都在球
的球面上,若
,
,
,
,则球
的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eaba7d7d6f2f3d6d4a2fe85d3c427f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-01-28更新
|
487次组卷
|
6卷引用:河南省信阳高级中学2021-2022学年高一下学期第三次月考数学试题
河南省信阳高级中学2021-2022学年高一下学期第三次月考数学试题江西省丰城市第九中学2023届高三复读班下学期开学质量检测数学(文)试题(已下线)微专题10 玩转外接球、内切球、棱切球经典问题(2)-【微专题】2022-2023学年高一数学常考点微专题提分精练(人教A版2019必修第二册)(已下线)专题强化三 多面体与球有关的内切、外接问题-2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(苏教版2019必修第二册)四川省遂宁市射洪中学校2023届高三下学期开学考试文科数学试题四川省成都市简阳实验学校2024届高三下学期开学考试数学(文)试题