名校
解题方法
1 . 如图所示棱锥P﹣ABCD中,底面ABCD是长方形,底面周长为8,PD=3,且PD是四棱锥的高.设AB=x.
(2)四棱锥外接球的表面积的最小值.
(2)四棱锥外接球的表面积的最小值.
您最近一年使用:0次
2022-05-20更新
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954次组卷
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7卷引用:13.3 空间图形的表面积和体积-2020-2021学年高一数学同步课堂帮帮帮(苏教版2019必修第二册)
(已下线)13.3 空间图形的表面积和体积-2020-2021学年高一数学同步课堂帮帮帮(苏教版2019必修第二册)广东省汕头市金山中学2020-2021学年高一下学期期中数学试题广东省广州市番禺区禺山中学2021-2022学年高二上学期10月月考数学试题湖南省湖湘教育三新探索协作体2019-2020学年高一上学期12月联考数学试题(已下线)13.3空间图形的表面积和体积-2021-2022学年高一数学10分钟课前预习练(苏教版2019必修第二册)山西省大同市浑源县第七中学校2022-2023学年高一下学期第三次月考数学试题(已下线)8.3简单几何体的表面积与体积——课后作业(基础版)
名校
解题方法
2 . 如图所示,三棱锥
中,
与
都是边长为
的正三角形.
![](https://img.xkw.com/dksih/QBM/2021/12/6/2866745284509696/2868074143694848/STEM/2eb559169e5b481aba77d69d58e89068.png?resizew=198)
(1)三棱锥
体积的最大值.
(2)若
,
,
,
四点都在球
的表面上,且球
的半径为
时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7853371cf04731c81a7a5dfd7a53b34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://img.xkw.com/dksih/QBM/2021/12/6/2866745284509696/2868074143694848/STEM/2eb559169e5b481aba77d69d58e89068.png?resizew=198)
(1)三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047616f1d1d39bf6c3cd07cf63ef5b80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a5d8831a9bef0f3d882d97d28e6d0e.png)
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21-22高二上·上海浦东新·期中
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3 . 已知正方体
.
到平面
的距离;
(2)在一个棱长为10的密封正方体盒子中,放一个半径为1的小球,任意摇动盒子,求小球在盒子中不能达到的空间的体积;
(3)在空间里,是否存在一个正方体,它的定点
到某个平面的距离恰好为0、1、2、3、4、5、6、7,若存在,求出正方体的棱长,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)在一个棱长为10的密封正方体盒子中,放一个半径为1的小球,任意摇动盒子,求小球在盒子中不能达到的空间的体积;
(3)在空间里,是否存在一个正方体,它的定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6cea2994db5fd94ec9193c76a4f3abb.png)
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2021-11-14更新
|
1885次组卷
|
4卷引用:上海市华东师范大学第二附属中学2021-2022学年高二上学期期中数学试题
(已下线)上海市华东师范大学第二附属中学2021-2022学年高二上学期期中数学试题(已下线)专题08几何体与球切、接的问题(练)--第一篇 热点、难点突破篇-《2022年高考数学二轮复习讲练测(新高考·全国卷)》(已下线)重难点02 几何体的表面积、体积、轴截面、多面体与球体内切外接问题 (重难点突破解题技巧与方法)-2022-2023学年高二数学考试满分全攻略(已下线)第二章 立体几何中的计算 专题二 空间距离 微点3 点到平面的距离(二)【培优版】
4 . 在四面体ABCD中,AB=BD=CD=1,AB⊥平面BCD,CD⊥BD,点M为AD上动点,连结BM,CM,如图.
![](https://img.xkw.com/dksih/QBM/2021/11/8/2846676231233536/2848045236518912/STEM/2e611f1c7e2a4701a5601e2c9023264e.png?resizew=227)
(1)求证:BM⊥CD;
(2)若AM=2MD,求二面角M﹣BC﹣D的余弦值;
(3)是否存在一个球,使得四面体ABCD的顶点都在此球的球面上?若存在,确定球心的位置并证明;若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/2021/11/8/2846676231233536/2848045236518912/STEM/2e611f1c7e2a4701a5601e2c9023264e.png?resizew=227)
(1)求证:BM⊥CD;
(2)若AM=2MD,求二面角M﹣BC﹣D的余弦值;
(3)是否存在一个球,使得四面体ABCD的顶点都在此球的球面上?若存在,确定球心的位置并证明;若不存在,请说明理由.
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5 . 已知直角梯形
,
,
,
,
,
为
的中点,
,如图(1),沿直线
折成直二面角,连结都分线段后围成一个空间几何体(如图2).
![](https://img.xkw.com/dksih/QBM/2021/10/12/2827846129442816/2829716966113280/STEM/6267868636554b04b3cf5df1b2b2e195.png?resizew=314)
(1)求异面直线
与
所成角的大小;
(2)求过
、
、
、
、
这五个点的球的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41aba1711910c6f533cc94319104f4fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60634341a9603e24b2bbc6960abe3d31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae341f580ff8fbf21f616fe900b0e4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/2021/10/12/2827846129442816/2829716966113280/STEM/6267868636554b04b3cf5df1b2b2e195.png?resizew=314)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)求过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
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名校
6 . 如图,在棱长为1的正方体
中.求:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/702d1e75-dde8-4bd5-9fc1-b80ba20d0b2b.png?resizew=154)
(1)直线
与
所成的角的大小;
(2)直线
与平面
所成的角的余弦值;
(3)正方体
的外接球体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/702d1e75-dde8-4bd5-9fc1-b80ba20d0b2b.png?resizew=154)
(1)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c597ff77c65c5add6f50294e3eee9536.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)正方体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
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2021-09-26更新
|
576次组卷
|
3卷引用:四川省成都第七中学2021-2022学年高二上学期入学数学(理科)试题
四川省成都第七中学2021-2022学年高二上学期入学数学(理科)试题四川省成都第七中学2021-2022学年高二上学期入学数学(文科)试题(已下线)考向31 与球有关的切、接应用问题(重点)-备战2022年高考数学一轮复习考点微专题(新高考地区专用)
名校
7 . 在直三棱柱
中,D,E,F分别为A1C1,AB1,BB1的中点.
![](https://img.xkw.com/dksih/QBM/2021/9/3/2800288467320832/2801518299717632/STEM/04e5ab86-e42a-4b38-b732-85084065c733.png?resizew=197)
(1)证明∶DE//平面B1BCC1;
(2)若AB=AC=AA1=2,AF⊥DE,求直三棱柱
外接球的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://img.xkw.com/dksih/QBM/2021/9/3/2800288467320832/2801518299717632/STEM/04e5ab86-e42a-4b38-b732-85084065c733.png?resizew=197)
(1)证明∶DE//平面B1BCC1;
(2)若AB=AC=AA1=2,AF⊥DE,求直三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
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2021-09-05更新
|
857次组卷
|
4卷引用:湖北省九师联盟2021-2022学年高三上学期8月开学考数学试题
名校
解题方法
8 . 如图所示,点
是边长为2的正方形
所在平面外一点,且
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/2021/9/1/2798708951703552/2799451002060800/STEM/ee7447b5-f79e-406d-8f31-82e98f833b77.png?resizew=228)
(1)求证:
;
(2)若二面角
与
的大小均为45°,求过
,
,
,
,
五点的球的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed66431681da1db8f7cb0f40cd19201.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a09d03d26008b17d89e98125eff110c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d19526cadbce0e984c2edc3f31d591.png)
![](https://img.xkw.com/dksih/QBM/2021/9/1/2798708951703552/2799451002060800/STEM/ee7447b5-f79e-406d-8f31-82e98f833b77.png?resizew=228)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edbf6462666c8015e7de28e344af30b2.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c911b404bbb8f8d5f1470585fa31ad97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47d294d69caac577339f11f477b2047e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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9 . 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
|
3卷引用:第15课时 课中 平面与平面垂直的性质
解题方法
10 . 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)
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