1 . 在三棱锥
中,
平面
,
,P为
内的一个动点(包括边界),
与平面
所成的角为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38593653bedb845ecfa820806a29a1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ecf072589c0f901d92f6bda111d841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a13b092fe451cdeaa95d3937fd866d67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1080295895df074480087279a84d7a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
A.![]() ![]() | B.![]() ![]() |
C.有且仅有一个点P,使得![]() | D.所有满足条件的线段![]() ![]() |
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7卷引用:山西省朔州市怀仁市2023-2024学年高三上学期第二次教学质量调研数学试题
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解题方法
2 . 如图,正四棱锥
每一个侧面都是边长为4的正三角形,若点M在四边形ABCD内(包含边界)运动,N为PD的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
A.当M为AD的中点时,异面直线MN与PC所成角为![]() |
B.当![]() ![]() |
C.当![]() ![]() |
D.存在一个体积为![]() ![]() |
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2卷引用:安徽省六安第一中学2023-2024学年高三下学期期末质量检测卷(二)数学试题
3 . 已知四面体
,
是边长为6的正三角形,
,二面角
的大小为
,则四面体
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/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/104be1b6811f391ac9b397b0a2be3e1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35c079889aea502b5783046f78728eb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/732250efe9c8c0cbca127fb2ed2a4bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6卷引用:浙江省杭州市2023-2024学年高三上学期期末数学试题
浙江省杭州市2023-2024学年高三上学期期末数学试题(已下线)专题2 球组合体 补体性质 练(已下线)浙江省绍兴市上虞区2022-2023学年高一下学期期末质量调研卷数学试题(已下线)专题04 立体几何初步-期期末真题分类汇编(人教A版2019必修第二册)(已下线)高一下学期期中复习选择题压轴题十七大题型专练(2)-举一反三系列(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)
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4 . 已知正三棱柱的侧面积为
.当这个正三棱柱的所有棱长之和最小时,它的外接球的表面积为__________
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52e9cb3cf2c44395ac26cd003f144828.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ce13774b09ff2edddaf21a072cf60a.png)
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5 . 正方体ABCD—A1B1C1D1的棱长为2,点E、F是平面A1B1C1D1内的动点,若
,AC⊥DF,现有以下四个命题:p:点E的轨迹是一个圆;q:点F的轨迹是一个圆;r:三棱锥F—A1BD的体积是定值;s:
.则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/600c2b2a205cc72c31bdda134bc60501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33793be9405b184ada8d98b0b1ef78a2.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 如图,已知正方体
的棱长为
为底面正方形
内(含边界)的一动点,则下列结论中:①若点
为
的中点,则
的最小值为
;②过点
作与
和
都成
的直线,可以作四条;③若点
为
的中点时,过点
作与直线
垂直的平面
,则平面
截正方体
的截面周长为
;④若点
到直线
与到直线
的距离相等,
的中点为
,则点
到直线
的最短距离是
.其中正确的命题有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/15/991e98f7-f97b-4672-82e1-668835677586.png?resizew=167)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc79c14b2ed75664547ddd8ba5b1be9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f23af5fccc4e374429b130a06570409.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e20838e72faf737614d76fcee82ab6c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7d857811cbd619f868d951aa7a0ab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c798204bbe306b3efd5bc9eae594c171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80427a12dc89e29aa067288684c4da67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/748ce363bf0d656545db3cc6c8d01690.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/15/991e98f7-f97b-4672-82e1-668835677586.png?resizew=167)
A.4个 | B.3个 | C.2个 | D.1个 |
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23-24高三上·四川成都·期末
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7 . 如图所示的几何体是由正方形
沿直线
旋转
得到的,设
是圆弧
的中点,
是圆弧
上的动点(含端点),则下列结论不正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/96e04b81-8576-4f01-bd73-2a68a34cdb85.png?resizew=148)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8192018a58bb1fe23769a48a4d9042ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdb53e0fdf3ebeb96e4f69feacbd80e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/17/96e04b81-8576-4f01-bd73-2a68a34cdb85.png?resizew=148)
A.存在点![]() ![]() |
B.存在点![]() ![]() |
C.存在点![]() ![]() ![]() |
D.存在点![]() ![]() ![]() ![]() |
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解题方法
8 . 在三棱锥
中,
,
,
为
的中点,
为
上一点,球
为三棱锥
的外接球,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebf91a833f6977fbefc242f8a8bbeef8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9151f36dc43515bc5f8f0a3728c4851.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
A.球![]() ![]() |
B.点![]() ![]() ![]() |
C.若![]() ![]() |
D.过点![]() ![]() |
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4卷引用:河南省驻马店市2023-2024学年高三上学期期末统一考试数学试题
河南省驻马店市2023-2024学年高三上学期期末统一考试数学试题 (已下线)专题13 棱台背景的立几综合湖北省黄冈市浠水县第一中学2024届高三下学期第一次高考模拟数学试题(已下线)第22题 球的切、接问题(高三二轮每日一题)
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解题方法
9 . 如图,正方体的棱长为2,点E是AB的中点,点P为侧面
内(含边界)一点,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/29553967-7a83-468b-a0e0-a94988882a37.png?resizew=162)
A.若![]() ![]() |
B.以D为球心,![]() ![]() ![]() |
C.若P为棱BC中点,则平面![]() ![]() |
D.若P到直线![]() ![]() |
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5卷引用:江西省九师联盟2024届高三上学期1月质量检测试数学试题
江西省九师联盟2024届高三上学期1月质量检测试数学试题江西省宜春市上高二中2024届高三上学期期末数学试题(已下线)专题13 棱台背景的立几综合(已下线)第三套 复盘卷(已下线)压轴小题7 探究立体几何中的动态问题
10 . 在平行四边形
中,已知
,将
沿
翻折得四面体
,作一平面分别与
交于点
,若四边形
是边长为
的正方形,则四面体
外接球的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a89c68029c5054f61ce8a7a7f0d95b8.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/d35dbf75101e6d032b64720fccfeaa46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9aa5a568de8ae6c1bfb5481775d6e5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c2d86d8daea5e652d99fe1c6bc3f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35dbf75101e6d032b64720fccfeaa46.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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