名校
解题方法
1 . 为弘扬中华民族优秀传统文化,某学校组织了《诵经典,获新知》的演讲比赛,本次比赛的冠军奖杯由一个铜球和一个托盘组成,如图①,已知球的体积为
,托盘由边长为4的正三角形铜片沿各边中点的连线向上折叠成直二面角而成,如图②.则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/15/bbf49297-f995-421e-a48f-987025f8d621.png?resizew=352)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67fb457e8ac0d3ac35e1c668ea138f91.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/15/bbf49297-f995-421e-a48f-987025f8d621.png?resizew=352)
A.经过三个顶点![]() ![]() ![]() ![]() |
B.平面![]() ![]() |
C.直线![]() ![]() ![]() |
D.球面上的点离球托底面![]() ![]() |
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名校
2 . 如图:棱长为
的正方体
的内切球为球
,
、
分别是棱
和棱
的中点,
在棱
上移动,则下列命题正确的是( )
①存在点
,使
垂直于平面
;
②对于任意点
,
平行于平面
;
③直线
被球
截得的弦长为
;
④过直线
的平面截球
所得的所有截面圆中,半径最小的圆的面积为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/5/d3253ceb-8f01-43b0-99a0-3c4f2785ee4f.png?resizew=165)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
①存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
②对于任意点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
③直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
④过直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddcfe70fcf6c4adf6fd7b02911c2cd36.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/5/d3253ceb-8f01-43b0-99a0-3c4f2785ee4f.png?resizew=165)
A.① | B.② | C.③ | D.④ |
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3 . 正三棱锥
的侧棱长为
,底面边长为
,则顶点
到底面
的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
4 . 如图,在棱长为
的正方体
中,
、
分别是棱
、
的中点,点
在线段
上运动,以下四个命题中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/21/13b56ced-a049-425d-bdb3-bcfc2f95b6fa.png?resizew=152)
A.平面![]() ![]() |
B.直线![]() ![]() ![]() |
C.存在点![]() ![]() |
D.![]() ![]() |
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解题方法
5 . 如图,棱长为2的正方体
中,点
分别是棱
的中点,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/42586cdf-1250-4e62-9147-6acfa10d74d6.png?resizew=164)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed906c3cc40665e9e6aace40cd4b7708.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/42586cdf-1250-4e62-9147-6acfa10d74d6.png?resizew=164)
A.直线![]() |
B.![]() ![]() |
C.过点![]() ![]() |
D.点![]() ![]() ![]() ![]() ![]() ![]() |
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2023-11-15更新
|
380次组卷
|
2卷引用:广东省深圳市福田区红岭中学2023-2024学年高二上学期期中数学试题
名校
6 . 如图,设正方体
的棱长为
,
为
的中点,
为
上的一个动点,设由点
、
、
构成的平面为
,则当点
与点
重合时,平面
截正方体的截面周长为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/5/f446f3e0-6738-4844-8f8c-002e815cf8d5.png?resizew=147)
您最近一年使用:0次
7 . 甲烷分子式为
,其结构抽象成的立体几何模型如图所示,碳原子位于四个氢原子的正中间位置,四个碳氢键长度相等,且任意两个氢原子等距排列,用
表示碳原子的位置,用
表示四个氢原子的位置,设
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eff19349a80467d65564cc2953f0c978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2dbca1604730621745c4bb6d4ccb051.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8cc5602408b0ae89990d8b07abe7235.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46902ee9fbd30111d7831f1fc7b79641.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/13/2e84f02a-f87d-418c-9675-306b9d5016ca.png?resizew=103)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-09-09更新
|
816次组卷
|
3卷引用:广东省深圳市南方科技大学附属中学2022-2023学年高二下学期期中数学试题
名校
8 . 设条件甲:直四棱柱
中,棱长都相等;条件乙:直四棱柱
是正方体,那么甲是乙的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
A.充分必要条件 | B.充分非必要条件 |
C.必要非充分条件 | D.既非充分也非必要条件 |
您最近一年使用:0次
2023-09-04更新
|
332次组卷
|
4卷引用:广东省深圳市第二高级中学2023-2024学年高二上学期第一学段考试数学试题
广东省深圳市第二高级中学2023-2024学年高二上学期第一学段考试数学试题广西桂林市桂林中学2020-2021学年高二下学期期中数学(理)试题(已下线)模块一 专题5 基本立体图形和直观图 讲(已下线)第八章 本章综合--归纳本章考点【第一课】“上好三节课,做好三套题“高中数学素养晋级之路
名校
9 . 已知正四面体
的棱长为
,其所有顶点均在球
的球面上.已知点
满足
,过点
作平面
平行于
和
,平面
分别与该正四面体的棱
相交于点
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fdf1c85ec23e1cf2a1983424d5211d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.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/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f52b9ece0ca7ab35f034163b90d6369.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ebcd61d7c928d37269eae4c75b09f51.png)
A.四边形![]() |
B.四棱锥![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() ![]() |
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解题方法
10 . 如图,正三棱锥
中,底面边长是3,棱锥的侧面积等于底面积的2倍,M是BC的中点.求:
(1)
的值;
(2)二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/14/c1912a26-d730-4653-83d7-834b17c48e69.png?resizew=172)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0e6383d9f658a784d322445554f3bc1.png)
(2)二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a5d8831a9bef0f3d882d97d28e6d0e.png)
您最近一年使用:0次