名校
解题方法
1 . 如图,在直三棱柱
中,
,
.
![](https://img.xkw.com/dksih/QBM/2022/9/12/3064881370423296/3066134020325376/STEM/aae63029e9094b7bbe50b06144b84441.png?resizew=240)
(1)设平面
与平面ABC的交线为l,判断l与AC的位置关系,并证明;
(2)求证:
;
(3)若
与平面
所成的角为30°,求三棱锥
内切球的表面积S.
![](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/f1240a927e5540d2dce76ba019f6cf82.png)
![](https://img.xkw.com/dksih/QBM/2022/9/12/3064881370423296/3066134020325376/STEM/aae63029e9094b7bbe50b06144b84441.png?resizew=240)
(1)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e862713d078c4f06ec1f15ccd6f5a1f7.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d38593653bedb845ecfa820806a29a1e.png)
您最近一年使用:0次
2022-09-14更新
|
1870次组卷
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6卷引用:必修二全册综合测试卷(提高篇)-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)必修二全册综合测试卷(提高篇)-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)模块五 专题2 全真能力模拟(人教B)(已下线)期末专题09 立体几何大题综合-【备战期末必刷真题】(已下线)宁夏回族自治区石嘴山市第三中学2022-2023学年高一下学期期末考试数学试卷宁夏石嘴山市第三中学2022-2023学年高一下学期期末数学试题山东省临沂市2021-2022学年高一下学期期末数学试题
解题方法
2 . 如图,在棱长为4的正方体
中,
为
的中点,经过
,
,
三点的平面记为平面
,点
是侧面
内的动点,且
.
,求证:
;
(2)平面
将正方体
分成两部分,求这两部分的体积之比
(其中
);
(3)当
最小时,求三棱锥
的外接球的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/6795cae2df43a722e1355e9562d93c09.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7146a372ce6a346fae937622a89d6589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/021a0a080f9ce719709a73a46c3459de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e0bdfd5676792840d607096ae0555b.png)
(2)平面
![](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/f737b04ce09bc7e1ed86dc9b3c85203b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1daf42c1a89bda5f17ce22e49dda533.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8049311621004b8d0f2637d13010db7.png)
您最近一年使用:0次
名校
3 . 已知直三棱柱
,
为线段
的中点,
为线段
的中点,
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/29/080eb1b1-7fed-4be0-aa0c-74cc46c784ff.png?resizew=175)
(1)证明:
;
(2)三棱锥
的外接球的表面积为
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2337fbebe5692bc3010040d93d2ec76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5f0cfc1049f84a04c81bd213afb8d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/29/080eb1b1-7fed-4be0-aa0c-74cc46c784ff.png?resizew=175)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7bd02e0adeae92ba9526261b1baf797.png)
(2)三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52753d89bf58589e2e83b19bd3d140b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb0f0d6b5ec8042d470609a00358d05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
您最近一年使用:0次
2023-01-14更新
|
1231次组卷
|
2卷引用:山东省枣庄市2022-2023学年高三上学期期末数学试题
名校
4 . 如图,点C在直径为AB的半圆O上,CD垂直于半圆O所在平面,平面ADE⊥平面ACD,且CD∥BE.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/eef206de-b81d-46fe-a5f9-088adbb04306.png?resizew=204)
(1)证明:CD=BE;
(2)若AC=1,AB=
,∠ADC=45°,求四棱锥A -BCDE的内切球的半径.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/eef206de-b81d-46fe-a5f9-088adbb04306.png?resizew=204)
(1)证明:CD=BE;
(2)若AC=1,AB=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
您最近一年使用:0次
2021-08-17更新
|
1347次组卷
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3卷引用:江西省新干中学2023届高三一模数学(理)试题
解题方法
5 . 已知矩形
中,
,
,
为线段
上一点(不在端点),沿线段
将
折成
,使得平面
平面
.
![](https://img.xkw.com/dksih/QBM/2021/6/22/2748470738575360/2782575554150400/STEM/7aa415d10a144504b48656715b5eabfe.png?resizew=338)
(1)证明:平面
与平面
不可能垂直;
(2)若二面角
大小为60°,
(ⅰ)求直线
与
所成角的余弦值;
(ⅱ)求三棱锥
的外接球的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68696b781af2609327222d22cb7bab3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58ebf8aa867ccca195ec94c3c96e9b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/2021/6/22/2748470738575360/2782575554150400/STEM/7aa415d10a144504b48656715b5eabfe.png?resizew=338)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae9bd3db15b3c5062240b4438fe6476.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e95fa1c3bcd3d0464fcadf248e90ace.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c35e8cf7b77cda3a23aaca62cd937f.png)
(ⅰ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9b123ae31090740589ba27a846620b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(ⅱ)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c586b72a984e1fd9082b9f02ef7f3e91.png)
您最近一年使用:0次
2021-08-09更新
|
917次组卷
|
4卷引用:第11章 简单几何体(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020必修第三册)
(已下线)第11章 简单几何体(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020必修第三册)浙江省温州市2020-2021学年高一下学期期末数学试题(A卷)(已下线)第二章 立体几何中的计算 专题六 几何体的外接球、棱切球、内切球 微点11 二面角的四面体模型【基础版】(已下线)第四章 立体几何解题通法 专题一 反证法 微点3 立体几何中的反证法综合训练【培优版】