解题方法
1 . 如图1,等腰梯形
,
.
沿
折起得到四棱锥
(如图2),G是
的中点.
![](https://img.xkw.com/dksih/QBM/2020/10/15/2571759312560128/2573149801177088/STEM/4b76fd412c90499d871e2c5d6ef3895a.png?resizew=176)
(1)求证
平面
;
(2)当平面
平面
时,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aeccc147f407f574f7d8efd7d0d0636.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d631f45bc652539853f236952afa5bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0bc34d1771fb14c101911660eaa075b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://img.xkw.com/dksih/QBM/2020/10/15/2571759312560128/2573149801177088/STEM/d0f908f6fe1d43dfaf7d8c4e3ddf7666.png?resizew=216)
![](https://img.xkw.com/dksih/QBM/2020/10/15/2571759312560128/2573149801177088/STEM/4b76fd412c90499d871e2c5d6ef3895a.png?resizew=176)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55537f7dbac74c17fe0dc386dcdab3fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fd45625bf31756fbaf1c415c6e5bf79.png)
(2)当平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a62a0adbe458148298b3dfb61c4373b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ff27eea7545bb06f9472f91290c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0fb98facc6b8400726136deadd3f1e7.png)
您最近一年使用:0次
解题方法
2 . 如图,四棱锥
的底面为平行四边形,平面
平面ABCD,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2020/7/3/2498163982155776/2500057368231936/STEM/a014cf8c6f4449eba60c566f90e34a8c.png?resizew=318)
(1)证明:
平面PAD,且
.
(2)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ad4c0ba3a6750537789844d0ec419d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a96d8b87b09e3ca52d91b3f24365f251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88197da08544c0dd0f8fb1359797ac9b.png)
![](https://img.xkw.com/dksih/QBM/2020/7/3/2498163982155776/2500057368231936/STEM/a014cf8c6f4449eba60c566f90e34a8c.png?resizew=318)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08f8b463fcecf0a757f386db56e074d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecf6c62979a7aa534a191d8387a741e8.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
2020-07-06更新
|
350次组卷
|
3卷引用:贵州省黔南州2019—2020学年度高二下学期期末考试数学(文)试题
名校
解题方法
3 . 如图,将直角边长为
的等腰直角三角形
,沿斜边上的高
翻折,使二面角
的大小为
,翻折后
的中点为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/b5713d59-db18-4c9c-8d44-34cde1186ca1.png?resizew=318)
(Ⅰ)证明
平面
;
(Ⅱ)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd29cc627d76412c236aac6b29fa0fdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/b5713d59-db18-4c9c-8d44-34cde1186ca1.png?resizew=318)
(Ⅰ)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ddb7c2ca1b6bee86cb24fed02e40da2.png)
(Ⅱ)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
2020-06-20更新
|
1050次组卷
|
7卷引用:贵州省贵阳市四校2021届高三上学期联合考试(一)数学(文)试题
解题方法
4 . 如图,在四棱锥P﹣ABCD中,底面ABCD为菱形,PA⊥底面ABCD,∠BAD=60°,AB=PA=4,E是PA的中点,AC,BD交于点O.
![](https://img.xkw.com/dksih/QBM/2020/4/29/2452056309514240/2452437202853888/STEM/5265d6c591b346beadde9eb750994606.png?resizew=183)
(1)求证:OE∥平面PBC;
(2)求三棱锥E﹣PBD的体积.
![](https://img.xkw.com/dksih/QBM/2020/4/29/2452056309514240/2452437202853888/STEM/5265d6c591b346beadde9eb750994606.png?resizew=183)
(1)求证:OE∥平面PBC;
(2)求三棱锥E﹣PBD的体积.
您最近一年使用:0次
名校
解题方法
5 . 如图,在四棱锥
中,平面
平面
,底面
为梯形,
,
,且
与
均为等边三角形,
为
的中点,
为
的外心.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/2d3f30a6-ac4a-4650-957a-9d74248c0bc8.png?resizew=188)
(1)求证:
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37591109b0a0ec5ffe2133f83310eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e7c4762381fa5fb173866d31b749d09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e2903ff33266528a7902ad51cf8d75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5e1441a49e782ff0ef46e776cde06a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6e2903ff33266528a7902ad51cf8d75.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/2d3f30a6-ac4a-4650-957a-9d74248c0bc8.png?resizew=188)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c05952cdf83c61053d809ce3f4487e39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/218054144a13435580cd132b9459546c.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c440fdd6a9db8fcbf6584dd03d0140a6.png)
您最近一年使用:0次
6 . 如图,四棱柱
的底面是直角梯形,
,
,
,四边形
和
均为正方形.
![](https://img.xkw.com/dksih/QBM/2020/2/9/2395195597750272/2395577642475520/STEM/d3415e3448824938887b5ba46d998f84.png?resizew=269)
(1)证明:平面
平面
.
(2)求四面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5acb763021bf166ca719d07223591d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25eb757d05fbff80d50c3bb8dbcb8657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://img.xkw.com/dksih/QBM/2020/2/9/2395195597750272/2395577642475520/STEM/d3415e3448824938887b5ba46d998f84.png?resizew=269)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a2e10a5aebe40a9018d5ee3ade7af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc8946b35564cd277227b80ef05c7f5.png)
您最近一年使用:0次
2020-02-09更新
|
442次组卷
|
3卷引用:2020届贵州省贵阳市高三11月联合考试数学(文)试题
7 . 如图所示,在梯形CDEF中,四边形ABCD为正方形,且
,将
沿着线段AD折起,同时将
沿着线段BC折起.使得E,F两点重合为点P.
![](https://img.xkw.com/dksih/QBM/2019/12/26/2363698988974080/2364051018088448/STEM/7d4585bd-bb04-4cd5-8fbc-6c947dd1adba.png)
(1)求证:平面
平面ABCD;
(2)求点D到平面PBC的距离h.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dabe6f02012bf9ca548dbb3f86d4cff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6830ebecddbd9759be626289c408e4f3.png)
![](https://img.xkw.com/dksih/QBM/2019/12/26/2363698988974080/2364051018088448/STEM/7d4585bd-bb04-4cd5-8fbc-6c947dd1adba.png)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
(2)求点D到平面PBC的距离h.
您最近一年使用:0次
2019-12-27更新
|
734次组卷
|
3卷引用:贵州省贵阳市普通高中2019-2020学年高三上学期期末监测考试数学(文)试题
8 . 在四棱锥
中,四边形
是直角梯形,
,
,
底面
,
,
,
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/772fb74b-364b-4883-98cd-19851abfbcf1.png?resizew=167)
(1)求证:平面
平面
;
(2)
上是否存在点
,使得三棱锥
的体积是三棱锥
体积的
.若存在,请说明
点的位置;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e0b7d845cbceccd3e76ca461fcc534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/011df06c6e64a1bb5e54ec12354b780f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/772fb74b-364b-4883-98cd-19851abfbcf1.png?resizew=167)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677d1863ff4d8ac1604b18149d4f320f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/142ea3931dc45cfe66b66ef17d3cefcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faac332bffea75e7b587596c3809278f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
13-14高三·全国·课后作业
名校
9 . 如图,一个三棱柱形容器中盛有水,且侧棱AA1=8,若侧面AA1B1B水平放置时,液面恰好过AC,BC,A1C1,B1C1的中点,当底面ABC水平放置时,液面高为多少?
您最近一年使用:0次
2018-10-18更新
|
1041次组卷
|
7卷引用:【全国百强校】贵州省遵义航天高级中学2018-2019学年高二上学期第一次月考数学(理)试题
【全国百强校】贵州省遵义航天高级中学2018-2019学年高二上学期第一次月考数学(理)试题(已下线)2015高考数学理一轮配套特训:7-1空间几何体结构及三视图和直观图人教A版(2019) 必修第二册 逆袭之路 第八章 8. 3 简单几何体的表面积与体积 小结(已下线)8.3 简单几何体的表面积与体积人教B版(2019) 必修第四册 北京名校同步练习册 第十一章 立体几何初步 11.1 空间几何体 11.1.6 祖暅原理与几何体的体积(二)人教A版(2019)必修第二册课本习题 习题8.3(已下线)8.3简单几何体的表面积与体积【第一练】“上好三节课,做好三套题“高中数学素养晋级之路