名校
解题方法
1 . 如图,在正四棱台
中,M,N,P,Q分别为棱AB,BC,
,
上的点.已知
,
,
,
,正四棱台
的高为6.
,NP相交于同一点.
(2)求正四棱台
挖去三棱台
后所得几何体的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188dfa1c5859c7d1084abe8adc559df6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60eb9136630cce58f21d8459f0bfb38a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/551b331edaf644682142ec4fcd217094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
(2)求正四棱台
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0e7905c14099a686ec5e3ed3bf01435.png)
您最近一年使用:0次
名校
2 . 如图,在四面体
中,
面
,
是
的中点,
是
的中点,点
在线段
上,
且
.
,求证:
平面
.
(2)若二面角
为
,求二面角
的余弦值.
(3)若三棱锥
的体积为1,求三棱锥
外接球的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6a2b112facda441f4e34bf5c145fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ad8d16722f5b9e7fd2602f14d5ffbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276e3c9755dbd39fb01de614840d230f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72221ee5b504d596ff799c0b356aa0ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ec2524be492bca0d1566bf848066f10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6eed8e6e9bea8c21b2688268f4fb7e6.png)
(3)若三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b1b8ad73dd13cb734206cfe15ada5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,在直三棱柱
中,P为
的中点,
,
,
.
(1)证明:
平面
.
(2)若四棱锥
的体积为12,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/188dfa1c5859c7d1084abe8adc559df6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d915b61de008ad2bf7818fc5eb3cfd15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d39d040c418bb3d2e002020dd3311c8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/7/8f11b86c-7323-4204-8636-7387a5f75436.png?resizew=122)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f61d8d0aaefc3ac491ad3659a2ba2f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2059a230ca1793fd4554b8d43e968f43.png)
(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b19ac275e614cda283f67a5c6cee2d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
您最近一年使用:0次
2023-07-06更新
|
210次组卷
|
2卷引用:湖南省衡阳市第一中学2022-2023学年高一下学期期末数学试题
4 . 如图所示,平面
平面
,四边形
为矩形,
,
,
,
.
(1)求多面体
的体积;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a5628323a7eeb11213df5c9048b3543.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bedde879f99aed69d745d5ec8fe62084.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/afc59fd5507a10eb2fcaa6ee8a04ce21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/27/c8b22850-b4b5-4616-af82-1c023ccdb17a.png?resizew=139)
(1)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99d65b5127ccd01345f8bca5d8a94bc4.png)
您最近一年使用:0次
2023-06-21更新
|
1017次组卷
|
3卷引用:2023年湖南省普通高中学业水平合格性考试数学试题(专家B卷)
5 . 如图,在直三棱柱
中,D是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/29136315-ec81-43aa-a85e-a81cf6daf1dc.png?resizew=179)
(1)求证:
平面
;
(2)若
,
,
,求几何体
的体积
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/29136315-ec81-43aa-a85e-a81cf6daf1dc.png?resizew=179)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/896e293411e2fd0da215ff20781cb36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba9e20d667d04bf3ee7f55cc795ce01.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883fc5e3faf39829d60804b59deb1730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/778ddb5cd565f3e96697aee202b9d510.png)
您最近一年使用:0次
2020-01-07更新
|
247次组卷
|
5卷引用:2017-2018学年湖南省衡阳县第三中学高二上学期期中考试数学(理)