名校
1 . 在四面体
中,
,四面体
的顶点均在球
的表面上,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e677be79bc6d0d98e10f8635f914d1af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.当二面角![]() ![]() ![]() | B.球![]() |
C.异面直线![]() ![]() | D.![]() ![]() ![]() |
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名校
2 . 在三棱锥
中,已知
,棱AC,BC,AD的中点分别是E,F,G,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13d28cb7181257cf732af4b615fc47d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c2539dc18fc736983e69dcc4a2b2f93.png)
A.过点E,F,G的平面截三棱锥所得截面是菱形 |
B.平面![]() |
C.异面直线AC,BD互相垂直 |
D.三棱锥![]() ![]() |
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3 . 如图1,在梯形
中,
,
是线段
上的一点,
,
,将
沿
翻折到
的位置.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/6/211d1e84-85c7-440e-972e-c6d64ffebc7f.png?resizew=616)
(1)如图2,若二面角
为直二面角,
,
分别是
,
的中点,若直线
与平面
所成角为
,
,求平面
与平面
所成锐二面角的余弦值的取值范围;
(2)我们把和两条异面直线都垂直相交的直线叫做两条异面直线的公垂线,点
为线段
的中点,
,
分别在线段
,
上(不包含端点),且
为
,
的公垂线,如图3所示,记四面体
的内切球半径为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eb15c7f8fd604976818ff6de254b6a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cff7399ecc698e2fb415147c96d0d03.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/6/211d1e84-85c7-440e-972e-c6d64ffebc7f.png?resizew=616)
(1)如图2,若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac9d5946fba71d0623ab27f24c6b57fa.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07e184efd65dfaa5d62242c482d2158d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf12905647aeeded72bbca21a63f319.png)
(2)我们把和两条异面直线都垂直相交的直线叫做两条异面直线的公垂线,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65bb1c5af4c7a9376882867e07690b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65bb1c5af4c7a9376882867e07690b18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da424b529ab73775b90cd4089d18419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba57d8c0d92f5b6bede99e8d9d227e40.png)
您最近一年使用:0次
解题方法
4 . 直三棱柱
中,
,
,
,
分别是棱
,
上一点,且
,若三棱锥
的外接球与三棱锥
的外接球外切,则
的长为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.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/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/157ab96c2f0461f7950c94c707e037cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51f73a0ca4e6c794242489066fddb6c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c0fd9a8e3c65cc498e577641817b00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
您最近一年使用:0次
5 . 在三棱锥
中,已知
,平面
平面
,二面角
的大小为
,则三棱锥
的外接球的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05a382548dfc016f6674e8848acd2337.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d294d69caac577339f11f477b2047e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
6 . 截角四面体是一种半正八面体,可由四面体经过适当的截角而得到.如图所示,将棱长为6的正四面体沿棱的三等分点作平行于底面的截面截角得到所有棱长均为2的截角四面体,则该截角四面体的体积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/8/5f753f8c-7be3-44af-9255-5cf25efe7c65.png?resizew=207)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/8/5f753f8c-7be3-44af-9255-5cf25efe7c65.png?resizew=207)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
7 . 已知圆台上、下底面半径分别为1,2,且上下底面圆周均在半径为
的球
的球面上,则该圆台的体积可能为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
8 . 祖暅是我国南北朝时期的数学家,著作《缀术》上论及多面体的体积:缘幂势既同,则积不容异——这就是祖暅原理.用现代语言可描述为:夹在两个平行平面之间的两个几何体,被平行于这个两个平面的任意平面所截,如果截得的两个截面的面积总相等,那么这两个几何体的体积相等.在棱长为2的正方体
中,
是
上一点,
于点
,
,点
绕
旋转一周所得圆的面积为_________ (用
表示);将空间四边形
绕
旋转一周所得几何体的体积为_________ .
![](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/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf271d6475f5305bc922677b4cfe28c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b5347307fa3258745446266a1104f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eabd5f3a86afe49dcd70571e2b96cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05581d61fac2783cc99b56b3bbc655f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
您最近一年使用:0次
2024-03-08更新
|
387次组卷
|
4卷引用:【一题多变】祖暅原理 曲面化直
解题方法
9 . 将四个半径为
的小球放入一个大球中,则这个大球半径的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
您最近一年使用:0次
10 . 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.![]() |
您最近一年使用:0次