1 . 已知正三棱锥的底面边长为
,高为
,则三棱锥的内切球的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 《九章算术》中记载,堑堵是指底面为直角三角形的直三棱柱,阳马是指底面为矩形且一条侧棱垂直于底面的四棱锥,如图,在堑堵
中,
,
=3,当阳马
的体积为8时,堑堵
的外接球表面积的最小值是( )
![](https://img.xkw.com/dksih/QBM/2021/7/9/2760252207202304/2790354858172416/STEM/8bcf37ae-ccdf-4ed8-9f42-273b740c0df8.png?resizew=218)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c04fc0cf6ff41f4e8e7a813b7b08b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfcd4aa8e2e84c4605a84097167e216a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://img.xkw.com/dksih/QBM/2021/7/9/2760252207202304/2790354858172416/STEM/8bcf37ae-ccdf-4ed8-9f42-273b740c0df8.png?resizew=218)
A.![]() | B.![]() | C.![]() | D.![]() |
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2021-08-20更新
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5卷引用:江西省新余市第四中学2021-2022学年高二上学期开学考试数学试题
3 . 《九章算术》中将底面是直角三角形的直三棱柱称之为“堑堵”,将底面为矩形,一条侧棱垂直于底面的四棱锥称之为“阳马”,在如图所示的堑堵
中,
,
,
,则在堑堵
中截掉阳马
后的几何体的外接球的表面积是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/af63513b-548f-4e20-a4a9-42017acf0e9c.png?resizew=166)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc81d42ad20eb0b0ca0807e5a4c3ceb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca36d4e1bef3b9205c3664c750be059.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895ac202e3507cb633337b41299ad84b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/af63513b-548f-4e20-a4a9-42017acf0e9c.png?resizew=166)
A.![]() | B.![]() | C.![]() | D.![]() |
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2卷引用:江西省南昌市八一中学、洪都中学等七校2020-2021学年高二下学期期中联考数学(文)试题
4 . 已知在矩形
中,
,
,将矩形
沿对角线
折成大小为
的二面角
,若折成的四面体
内接于球
,则下列说法错误的是( )
![](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/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c909cd1b6f3fa1ec39eb245e8f5c11c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.四面体![]() ![]() | B.球的体积随![]() |
C.球心![]() | D.球![]() ![]() |
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解题方法
5 . 已知三棱锥
中,
平面
,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/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e222783b26628b69e3923d5247c9ae9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6卷引用:江西省铜鼓中学2020-2021学年高二(实验班)上学期数学(文)试题
江西省铜鼓中学2020-2021学年高二(实验班)上学期数学(文)试题广东省茂名市五校联盟2020-2021学年高一下学期期末数学试题四川省眉山市彭山区第一中学2022-2023学年高二上学期第二次月考数学(文)试题(已下线)专题21 外接球与内接球相关模型-【重难点突破】2021-2022学年高一数学常考题专练(人教A版2019必修第二册)广东省茂名化州市第一中学2021-2022学年高一下学期6月月考数学试题广东省韶关市曲江区曲江中学2021-2022学年高一下学期期末复习1数学试题
解题方法
6 . 在三棱锥A-BCD中,平面ABD⊥平面BCD,BD⊥CD,且AB=BD=DA=3,
,则三棱锥A-BCD的外接球的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18120a244d3a1f9c1688bf53eb2ad775.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6卷引用:江西省赣州市教育发展联盟2021-2022学年高二上学期第7次联考高二数学(文)试题
江西省赣州市教育发展联盟2021-2022学年高二上学期第7次联考高二数学(文)试题江苏省徐州市2020-2021学年高一下学期期末数学试题(已下线)专题21 外接球与内接球相关模型-【重难点突破】2021-2022学年高一数学常考题专练(人教A版2019必修第二册)(已下线)第8章 立体几何初步(压轴30题专练)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)(已下线)高一数学下学期期末精选50题(压轴版)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)江苏省徐州市2023-2024学年高一下学期第一次质量检测数学试题(1)
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解题方法
7 . 在长方体
中,
,
,
分别为
,
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7eca2ce72ab61c34ed2a7b24314476.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/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbafedc202bd0d86c4dfdece9f8f4fe.png)
A.![]() |
B.三棱锥![]() ![]() |
C.三棱锥![]() ![]() |
D.直线![]() ![]() ![]() |
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2卷引用:江西省南昌市豫章中学2021-2022学年高二入学调研(B)数学(文)试题
8 . 如图,已知正四棱柱
的底面边长为1,侧棱长为2,点
,
分别在半圆弧
,
(均不含端点)上,且
,
,
,
在球
上,则下列命题:①当点
在
的三等分点处,球
的表面积为
;②当点
在
的中点处,过
,
,
三点的平面截正四棱柱所得的截面的形状都是四边形;③当点
在
的中点处,三棱锥
的体积为定值.其中真命题的个数为( )
![](https://img.xkw.com/dksih/QBM/2021/5/8/2716620314402816/2760012286189568/STEM/54e68261-b039-4ed2-b4a0-c0f0b2d6c351.png?resizew=179)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8185664b888e7dbce32f1e7ce066595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd0d603b80beb24ab50c7aea63aed8e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd0d603b80beb24ab50c7aea63aed8e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d18fee1ebc15528a688bb602ad70098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8185664b888e7dbce32f1e7ce066595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8185664b888e7dbce32f1e7ce066595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b34c18ab18eed9379c0026de1ce892e.png)
![](https://img.xkw.com/dksih/QBM/2021/5/8/2716620314402816/2760012286189568/STEM/54e68261-b039-4ed2-b4a0-c0f0b2d6c351.png?resizew=179)
A.3 | B.2 | C.1 | D.0 |
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9 . 已知棱长为6的正方体的所有顶点均在球O的球面上,则球O的表面积为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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2021-07-12更新
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198次组卷
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2卷引用:江西省吉安市第三中学2021-2022学年高二9月份开学考试数学(理)试题
2021·全国·模拟预测
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10 . 已知在三棱锥
中,
,
,则该三棱锥内切球的体积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/292d0b9ce587bd5df884a988c22ccba2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a31523cd35ebc290365cde9b02d127e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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