名校
解题方法
1 . 在三棱锥A-BCD中,E,F分别是棱BC,CD上的点,且
平面ABD.
![](https://img.xkw.com/dksih/QBM/2021/12/26/2887270960095232/2927470886961152/STEM/12f3d43a-0b22-4d9f-8b9a-39d8d7f9afaa.png?resizew=194)
(1)求证:
平面AEF;
(2)若
平面BCD,
,
,记三棱锥F-ACE与三棱锥F-ADE的体积分别为
,
,且
,求三棱锥B-ADF的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7a407b262c22419f73396170ecdc849.png)
![](https://img.xkw.com/dksih/QBM/2021/12/26/2887270960095232/2927470886961152/STEM/12f3d43a-0b22-4d9f-8b9a-39d8d7f9afaa.png?resizew=194)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e3c0430146b7b8d40ebb721a4d0de19.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bffd657e48b15b9b54a55817e2c26b22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dac9a2626064adb81edc2bbf36cb1d65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e449727158281e3370255436481a848.png)
您最近一年使用:0次
2022-03-02更新
|
1230次组卷
|
7卷引用:山西省晋中市2021届高三三模数学(文)试题
名校
解题方法
2 . 已知直三棱柱
中,
,点D是AB的中点.
平面
;
(2)若底面ABC边长为2的正三角形,
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb689000fa7a3b425be3196d8b0f32af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd209cc3f91b254f5ed934e89271e0e.png)
(2)若底面ABC边长为2的正三角形,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c90ff9402bacab8319385d3bab70dcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91d6c98b5ed325bea4a4897a60cb1c12.png)
您最近一年使用:0次
2022-01-25更新
|
1942次组卷
|
14卷引用:江苏省镇江中学2020-2021学年高二上学期期末数学试题
江苏省镇江中学2020-2021学年高二上学期期末数学试题2015届贵州省贵阳市普通高中高三上学期期末监测考试文科数学试卷黑龙江省鹤岗市第一中学2016-2017学年高一下学期期末考试数学(文)试题黑龙江省八校2021-2022学年高三上学期期末联合考试数学(文)试题广东省中山市2021-2022学年高一下学期期末数学试题甘肃省兰州市第五十七中学2022-2023学年高三下学期开学模拟考试(文科)数学试题(已下线)广东省佛山市南海区桂城中学2022-2023学年高一下学期第三次大测数学试题(已下线)期末复习06 空间几何线面、面面平行-期末专项复习(已下线)高一下学期数学期末押题卷-期末专项复习陕西省咸阳市武功县普集高级中学2022-2023学年高一下学期6月第三次月考数学试题湖南省长沙市实验中学2022-2023学年高一下学期期末数学试题福建省诏安第一中学2022-2023学年高一下学期期末冲刺数学试题江西省丰城中学2023-2024学年高一(创新班)上学期第一次段考(10月)数学试题(已下线)期末测试卷02-《重难点题型·高分突破》(人教A版2019必修第二册)
3 . 如图,如图,在四棱锥
中,底面
为平行四边形,
,
,且
底面
.
平面
;
(2)求
到平面
的距离.
![](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/f80f51c31583fea58fde645474d60b8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3f15f3725dc69af03fb68c639796c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2022-04-01更新
|
1067次组卷
|
6卷引用:江苏省南京师范大学苏州实验学校2021-2022学年高一日新班上学期12月月考数学试题
名校
解题方法
4 . 如图所示,正方体
中,棱长为2,且
分别为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/aaa0aac4-60f4-4946-a384-27689fd0ae18.jpg?resizew=184)
(1)求证:
∥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/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31be3b7305d6c181420ea7b28c420851.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/12/aaa0aac4-60f4-4946-a384-27689fd0ae18.jpg?resizew=184)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55ba1f8922a40840d56b1e9b3ae72a5b.png)
(2)求四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44a4854ccdf3fefecfb95e70f1f1a5f0.png)
您最近一年使用:0次
2021-08-04更新
|
499次组卷
|
3卷引用:黑龙江省大庆市2021届高三二模数学(文)试题
黑龙江省大庆市2021届高三二模数学(文)试题陕西省榆林市神木中学2020-2021学年高二下学期第四次测试文科数学试题(已下线)专题19 立体几何(解答题)-备战2022年高考数学(文)母题题源解密(全国甲卷)
名校
解题方法
5 . 如图所示,在多面体BCAEFD中,矩形BCFE所在平面与直角梯形AEFD所在平面垂直,
,
,G为CD的中点,且
,
.
![](https://img.xkw.com/dksih/QBM/2022/1/19/2897976763924480/2904886588850176/STEM/a67be6ce-f258-4590-adc9-7f4d3090a893.png?resizew=297)
(1)求证:
平面BCFE;
(2)求多面体BCAEFD的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/751ecec223e69ea940ffe196aa1463ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce726bceb02452bb4e5ed6b00fa94e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eb54f503cec93e3deb00f3dd70dbc4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ade06068471a9d76e32b417bef7551.png)
![](https://img.xkw.com/dksih/QBM/2022/1/19/2897976763924480/2904886588850176/STEM/a67be6ce-f258-4590-adc9-7f4d3090a893.png?resizew=297)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ff5ec52d9348020f5380e2de82e769.png)
(2)求多面体BCAEFD的体积.
您最近一年使用:0次
2022-01-29更新
|
521次组卷
|
2卷引用:河南省新乡县龙泉高级中学2021-2022学年高三上学期11月半月考数学(文)试题
解题方法
6 . 如图,在多面体
中,四边形
是矩形,四边形
为等腰梯形,且
,
,
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/21afb801-f2d2-49d2-8157-41f9bcea9cc7.png?resizew=173)
(1)求证:
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c91baecb97fadd4f8ab49e6effcbc04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc39144b305c67d44410d41053a1d28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f3f687d101e7d54af2348c7a3277778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/21afb801-f2d2-49d2-8157-41f9bcea9cc7.png?resizew=173)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a598a35e6a4bfb3a5f08b55b70bdc3.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/437c9774700f6c066b3e19d17d54b368.png)
您最近一年使用:0次
2021-11-25更新
|
633次组卷
|
3卷引用:黑龙江省龙东地区四校2021-2022学年 高三上学期联考数学(理)试题
黑龙江省龙东地区四校2021-2022学年 高三上学期联考数学(理)试题(已下线)解密09 立体几何初步(分层训练)-【高频考点解密】2022年高考数学二轮复习讲义+分层训练(浙江专用)四川省眉山市仁寿县铧强中学2023-2024学年高三上学期10月诊断性考试文科数学试题
名校
解题方法
7 . 如图所示,几何体
中,
是正三角形,
,
均与面
垂直,且
,点
、
分别在棱
、
上,满足
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/4aff93f7-04da-42a1-91d5-133bd6c8e11a.png?resizew=169)
(1)求证:
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1d97b95bccd80f06c3af864897da9a.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/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a798ddf34f0fed7cb1616228cc88936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d65734b86acbb1df7057b72cbf6dcb4f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/23/4aff93f7-04da-42a1-91d5-133bd6c8e11a.png?resizew=169)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9c68879985182b4de065c552cb8e31.png)
您最近一年使用:0次
2021-07-15更新
|
390次组卷
|
2卷引用:江西省景德镇一中2020-2021学年高二下学期期末数学(文)试题
名校
解题方法
8 . 如图,在四棱锥
中,PD⊥平面ABCD,四边形ABCD是等腰梯形,
,
,
,M,N分别是AB,AD的中点.
![](https://img.xkw.com/dksih/QBM/2022/1/23/2900630376054784/2919654224412672/STEM/a11f38b6-d954-43e5-bb5f-c1a63f711f8f.png?resizew=198)
(1)证明:平面PMN⊥平面PAD;
(2)若二面角
的大小为60°,求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd8e727e4efc22b49649f71ae9c9d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/903e252094f04331047fe92335aac7b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://img.xkw.com/dksih/QBM/2022/1/23/2900630376054784/2919654224412672/STEM/a11f38b6-d954-43e5-bb5f-c1a63f711f8f.png?resizew=198)
(1)证明:平面PMN⊥平面PAD;
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10f7a0ab16cbb95691b3d80334a91401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
2022-02-19更新
|
1099次组卷
|
7卷引用:重难点 03 空间向量与立体几何-2021年高考数学(理)【热点·重点·难点】专练
(已下线)重难点 03 空间向量与立体几何-2021年高考数学(理)【热点·重点·难点】专练江西省赣州市赣县第三中学2020-2021学年高二2月入学考试数学(理)试题广东省七校联合体2020-2021学年高二下学期2月联考数学试题河北省邯郸市2021届高三上学期期末质量检测数学试题广东省梅州市丰顺县、五华县2022届高三上学期一模数学试题(已下线)重难点03 立体几何与空间向量-2022年高考数学【热点·重点·难点】专练(全国通用)湖南省常德市临澧县第一中学2022届高三下学期一模数学试题
名校
解题方法
9 . 如图,四棱锥
的底面是正方形,侧面PAD是正三角形,
,且侧面
底面ABCD,E为侧棱PD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/af8736a2-5fde-47e4-84ea-02347d4d679c.png?resizew=215)
(1)求证:
平面EAC;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/af8736a2-5fde-47e4-84ea-02347d4d679c.png?resizew=215)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acf2bc3dd1f1ae5d5e28b0366f454ec1.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d00bae294d76d2cfaf11520e20409c05.png)
您最近一年使用:0次
2022-02-21更新
|
2773次组卷
|
2卷引用:内蒙古自治区阿拉善盟第一中学2021-2022学年高二上学期期中考试数学(文)试题
解题方法
10 . 如图,多面体
中,
,
,
,
,
平面
,
,
分别为
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/94525b1b-eae9-45b7-b6a6-c5a9ac5d232d.png?resizew=169)
(1)证明:
平面
;
(2)证明:
平面
;
(3)求平面
将多面体
分成上、下两部分的体积比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883fc5e3faf39829d60804b59deb1730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0082d25fc347d093ca69e6e0992f6e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c86d9bc5d20695ac6b9398eeec4ec7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/94525b1b-eae9-45b7-b6a6-c5a9ac5d232d.png?resizew=169)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b78172568aac9805d2ea2d5f742bf80c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d2d217e9bcd059908f117dfc4d4259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62fd0b510920be6bc60d170c3ff3da3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
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