名校
解题方法
1 . 中国正在由“制造大国”向“制造强国”迈进,企业不仅仅需要大批技术过硬的技术工人,更需要努力培育工人们执着专注、精益求精、一丝不苟、追求卓越的工匠精神,这是传承工艺、革新技术的重要基石.如图所示的一块木料中,
是正方形,
平面
,
,点
,
是
,
的中点.
和棱
将木料锯开,在木料表面应该怎样画线,请说明理由并计算截面周长;
(2)若要经过点B,E,F将木料锯开,在木料表面应该怎样画线,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.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/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)若要经过点B,E,F将木料锯开,在木料表面应该怎样画线,请说明理由.
您最近一年使用:0次
2023-04-19更新
|
2740次组卷
|
7卷引用:专题16空间向量与立体几何(解答题)
名校
2 . 如图,边长是6的等边三角形
和矩形
.现以
为轴将面
进行旋转,使之形成四棱锥
,
是等边三角形
的中心,
,
分别是
,
的中点,且
,
面
,交
于
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/3197f79c-594b-42ed-a13b-b61964f1bf7d.png?resizew=233)
(1)求证
面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e74395b07e8153a0ef0bbcb5881013f.png)
(2)求
和面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db2b1c641b93caae9b7a82441e4ba70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f6719c1d339ec50a9bf36b26af7258b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a78b6fb582468bdd5c3afa5461aefce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa7bbd7831e9ff4f8cffc8889d34f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/3197f79c-594b-42ed-a13b-b61964f1bf7d.png?resizew=233)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d1ed33ef4004d6a7d2eeb6ccd113479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e74395b07e8153a0ef0bbcb5881013f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e74395b07e8153a0ef0bbcb5881013f.png)
您最近一年使用:0次
2023-01-14更新
|
2416次组卷
|
7卷引用:辽宁省葫芦岛市第一高级中学2022-2023学年高三上学期期末数学试题
辽宁省葫芦岛市第一高级中学2022-2023学年高三上学期期末数学试题第8章 立体几何初步 章末测试(基础)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)专题8.16 空间角大题专项训练(30道)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)(已下线)第04讲 利用几何法解决空间角和距离19种常见考法归类(2)(已下线)模块五 期末重组篇 专题7重庆市2023届高三下学期3月月度质量检测数学试题(已下线)13.2.3 直线和平面的位置关系(1)
3 . 如图,边长为4的两个正三角形
,
所在平面互相垂直,E,F分别为BC,CD的中点,点G在棱AD上,
,直线AB与平面
相交于点H.
;②直线HE,GF,AC相交于一点;
注:若两个问题均作答,则按第一个计分.
(2)求直线BD与平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a100d3638f0f04db2bd262c051f59b2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e011e5a622d961d9174ebce34c6ee033.png)
注:若两个问题均作答,则按第一个计分.
(2)求直线BD与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
您最近一年使用:0次
2024-03-21更新
|
2124次组卷
|
6卷引用:江苏省扬州市2024届高三第二次调研测试数学试题
江苏省扬州市2024届高三第二次调研测试数学试题江苏省泰州市2024届高三第二次调研测试数学试题(已下线)江苏省南通市2024届高三第二次调研测试数学试题变式题 16-19(已下线)江苏省泰州市2024届高三第二次调研测试数学试题变式题16-19江苏省南通市2024届高三第二次调研测试数学试题(已下线)模块三 专题3 高考新题型专练 专题1 劣构题专练(苏教版)
2023高三·全国·专题练习
解题方法
4 . 如图,在棱长都等于1的三棱锥
中,
是
上的一点,过
作平行于棱
和棱
的截面,分别交
,
,
于
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/4/556ce754-80b9-4b09-869d-9a25bf48bfc4.png?resizew=181)
(1)证明截面
是矩形;
(2)
在
的什么位置时,截面面积最大,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/4/556ce754-80b9-4b09-869d-9a25bf48bfc4.png?resizew=181)
(1)证明截面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
您最近一年使用:0次
名校
解题方法
5 . 如图,四边形
与
均为菱形,
,
,
,记平面
与平面
的交线为
.
;
(2)证明:平面
平面
;
(3)记平面
与平面
夹角为
,若正实数
,
满足
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f84f169e50dc59d4f7a8e1e36f5c847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf80b036459da6dcb841a4bbe3859fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d223346f234798b92bd1eaa78360b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef7ce5d5cc777ef4d5b890cc9cbb70b0.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1b6711e6dd48be6cf8fa52926924d21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)记平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b7195a853621ea5bebe8d2d1436732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b992104248a854e6e033c26602aff813.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7bfbdbf0f1957459f12ae149d5176e.png)
您最近一年使用:0次
2023-07-11更新
|
1923次组卷
|
5卷引用:四川省成都外国语学校2023-2024学年高二上学期10月月考数学试题
名校
解题方法
6 . 若正四面体
的顶点都在一个表面积为
的球面上,过点
且与
平行的平面
分别与棱
交于点
,则空间四边形
的四条边长之和的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997b5842f3d4eae1989debee9ae41b9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/9df7fc746f8c4801d8f2f0471ba3297e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28d6477c85c5a4ac410a884e92fbe53.png)
您最近一年使用:0次
2024-02-21更新
|
1296次组卷
|
5卷引用:上海外国语大学附属浦东外国语学校2024届高三下学期3月月考数学试题
名校
解题方法
7 . 已知正四面体
的棱长为3,其外接球的球心为
.点
满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f322f8f148fbbaa38b6c0218ae68fe.png)
,过点
作平面
平行于
和
,设
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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f322f8f148fbbaa38b6c0218ae68fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8b50bf37cfd8cecf855ea7a817b0cd.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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
A.四边形![]() | B.当![]() ![]() |
C.当![]() ![]() ![]() ![]() | D.四棱锥![]() ![]() |
您最近一年使用:0次
2022-03-09更新
|
2402次组卷
|
4卷引用:福建省福州市2022届高三3月质量检测数学试题
福建省福州市2022届高三3月质量检测数学试题(已下线)押新高考第12题 立体几何-备战2022年高考数学临考题号押题(新高考专用)辽宁省大连育明高级中学2022届高三第一次模拟考试数学试卷辽宁省实验中学2022-2023学年高三上学期期中数学试题
解题方法
8 . 如图,在正四面体中,棱
的中点为M,棱
的中点为N,过
的平面交棱
于P,交棱
于Q,记多面体
的体积为
,多面体
的体积为
,则( )
A.直线![]() ![]() | B.![]() |
C.点C与点D到平面![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
9 . 由两个全等的正四棱台组合而得到的几何体1如图1,沿着
和
分别作上底面的垂面,垂面经过棱
的中点
,则两个垂面之间的几何体2如图2所示,若
,则()
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81466f1b48314cc70b8a0244ecf88439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/670f6380f5fcdcf117eba37e2186d87b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40551c737cd56c64be0c884e810afd94.png)
A.![]() | B.![]() |
C.![]() ![]() | D.几何体2的表面积为![]() |
您最近一年使用:0次
2023-08-01更新
|
1045次组卷
|
5卷引用:江西省南昌市2022-2023学年高一下学期期末调研检测数学试题
江西省南昌市2022-2023学年高一下学期期末调研检测数学试题四川省兴文第二中学校2023-2024学年高二上学期开学考试数学试题湖南省长沙市长郡中学2024届高三上学期月考(一)数学试题湖南省长沙市长郡中学2024届高三上学期月考(五)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)
名校
10 . 如图,圆柱的轴截面
为正方形,点
在底面圆周上,且
为
上的一点,且
为线段
上一动点(不与
重合)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/13/154f5638-5181-4e3f-93c1-33127df3bef6.png?resizew=154)
(1)若
,设平面
面
,求证:
;
(2)当平面
与平面
夹角为
,试确定
点的位置.
![](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/2675e2171c51891dc71f4284cda8a270.png)
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(1)若
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(2)当平面
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2022-10-11更新
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