1 . 如图,多面体
中,
是菱形,
,
平面
,
,且
.
![](https://img.xkw.com/dksih/QBM/2022/10/25/3095557210415104/3100309961850880/STEM/eeeaab36bd044f6eafe1b031a31bfe9c.png?resizew=186)
(1)求证:平面
平面
;
(2)求多面体
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/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/147e7c8ba0bbb540a712f6eb2ed6d22e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b834d2394d1779d267e305df5f5d43d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d552b00c85d1e11ef3ac6b6e06221fa.png)
![](https://img.xkw.com/dksih/QBM/2022/10/25/3095557210415104/3100309961850880/STEM/eeeaab36bd044f6eafe1b031a31bfe9c.png?resizew=186)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3547a914468b082d8d8741b974a03190.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6439082496df7567acd5a31a3448db71.png)
(2)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
您最近一年使用:0次
2022-11-01更新
|
1393次组卷
|
4卷引用:广西普通高中2023届高三上学期摸底考试数学(文)试题
广西普通高中2023届高三上学期摸底考试数学(文)试题广西南宁市第三十六中学2023届高三上学期数学(文)第三次检测试题(已下线)模块十一 立体几何-1(已下线)第31讲 空间几何体体积及点到面的距离问题4种题型
2 . 在如图所示的多面体
中,
平面
,
,
,
,点
、
分别为
、
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/5e9433b6-7d2a-4cb2-afa5-c14f8b08a79b.png?resizew=123)
(1)求证:平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b0b0494b994fa27ec55342e840b785.png)
平面
;
(2)求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2edf249d1bd71b64bdc2e0f9b0a320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c75d8581bb7b2a91795852acdc07d68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31b2cc1d0bfd22c88286880b9da1f6f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c17e8641c9d0539012685f26a098b2bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/28/5e9433b6-7d2a-4cb2-afa5-c14f8b08a79b.png?resizew=123)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b0b0494b994fa27ec55342e840b785.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a0d238b6e9b49bbea22a79402e8e4f.png)
(2)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2edf249d1bd71b64bdc2e0f9b0a320.png)
您最近一年使用:0次
3 . 如图所示,在四棱锥
中,平面
平面
,
,
是等边三角形,已知
,
,M是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/895864e8-4f66-4fb1-b889-1b606119873c.png?resizew=192)
(1)证明:平面
平面
;
(2)求四棱锥
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/ee8ef58be8708144272538ee427fb92c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58579094b5d753e9205c2ec89ca3ae07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5e8d9bd81b063a824baf17d947db5ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/895864e8-4f66-4fb1-b889-1b606119873c.png?resizew=192)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6fb16d2f0db758b8b7a8d3743143f48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4117625867a74cd022584500c76deca.png)
您最近一年使用:0次
解题方法
4 . 如图,已知四棱锥
的底面是边长为1的正方形,
底面
且
,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/250281e0-6c6d-4d0f-a68d-ff92025b544b.png?resizew=169)
(1)求证:
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4117625867a74cd022584500c76deca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39967d6f3aed6ce7b6643787795d451d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca7f2c76e2d7aafeafbba1f7d740850e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/250281e0-6c6d-4d0f-a68d-ff92025b544b.png?resizew=169)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a10ec513600c19b4bd140ce3da17355.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49c2bd5eaf71f8866c0979fa299df50d.png)
您最近一年使用:0次
解题方法
5 . 如图,在三棱锥
中,
,
,O为AC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/6/d0855741-8ac8-43bb-a658-d5284af43db3.png?resizew=220)
(1)证明:PO⊥平面ABC;
(2)若点M在棱BC上,且MC=2MB,求点C到平面POM的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca9de4b28493cb6f8fc83cf294c5cc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/6/d0855741-8ac8-43bb-a658-d5284af43db3.png?resizew=220)
(1)证明:PO⊥平面ABC;
(2)若点M在棱BC上,且MC=2MB,求点C到平面POM的距离.
您最近一年使用:0次
6 . 如图在四棱锥
中,四边形
为平行四边形,
,
为
的中点,且
,
底面
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/5cf44b2e-14df-43ca-a01c-a55961857ac3.png?resizew=221)
(1)证明:平面
平面
;
(2)求四棱锥
的体积.
![](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/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48e69a19dd11c933e9e42bf6f8b8550f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/5cf44b2e-14df-43ca-a01c-a55961857ac3.png?resizew=221)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6edfd337101a5c034ccbab0380727154.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
7 . 如图所示,在空间几何体ABCDE中,△ABC与△ECD均为等边三角形,
,
,且平面ABC和平面CDE均与平面BCD垂直.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/2081d74a-7e43-4d68-9043-04ae9016e34b.png?resizew=143)
(1)求证:平面ABC
平面ECD;
(2)求空间几何体ABCDE的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e98937d07d10a81acd67acebb25633.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32ad76a622b81e3eaf345f8100dd1885.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/2081d74a-7e43-4d68-9043-04ae9016e34b.png?resizew=143)
(1)求证:平面ABC
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8acbf7aa8e684b3bb898396d8de8a58e.png)
(2)求空间几何体ABCDE的体积.
您最近一年使用:0次
名校
解题方法
8 . 如图,四棱锥
中,底面ABCD为直角梯形.
,
,
,
,
为等边三角形,平面
平面ABCD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/e431c863-ccb6-4fc8-bd6b-3a1bcacd7239.png?resizew=196)
(1)若M为PB的中点,证明:
面PAD;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6be2b61f4a38e2ee2c1a01e00b3ae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90e70d5be99ab8b058ff2fb4d8c3d0d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2970d638e7993b609106d2ddd65e591.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de5de3b01f3c591a845ffa206675b882.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4020b47658346639e42836fea8e672c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2c4cc37d6ba218107c9c5d820740fc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/e431c863-ccb6-4fc8-bd6b-3a1bcacd7239.png?resizew=196)
(1)若M为PB的中点,证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa14afe6f0aad22e8e869c39a60be657.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df34afa61d3324211e4cba4fc4bf2e4d.png)
您最近一年使用:0次
2022-10-21更新
|
616次组卷
|
3卷引用:广西南宁市2023届高三上学期摸底测试数学(文)试题
9 . 如图所示,在四棱柱
中,底面
是等腰梯形,
,
,
,侧棱
⊥底面
且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/15/f44ca6e0-bf5d-4599-bfdf-ff928725ac24.png?resizew=173)
(1)指出棱
与平面
的交点
的位置(无需证明);
(2)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7ddbb49c644bf06ccbad885ba2c84a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db886994f0a7ddfeb0fe2d7099d4498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb8781b3e04f90bde1fd8a96075ab932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161f651ef002ac85870d46b04347b54f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5493b3fbfbf3d2ec8c57fe228d8047cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/15/f44ca6e0-bf5d-4599-bfdf-ff928725ac24.png?resizew=173)
(1)指出棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb16f7dbc4b9993c4efa0764df1d8ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69c66600644e8bdff1728bf2c7e5375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252053b853152bd294a8315debd00b92.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da9dcf6c319174c9ea2b1ceaed1649a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69c66600644e8bdff1728bf2c7e5375.png)
您最近一年使用:0次
2022-10-19更新
|
483次组卷
|
3卷引用:广西2022届高三高考桂柳鸿图综合模拟金卷(2)数学(文)试题
名校
解题方法
10 . 如图,在三棱柱
中,
平面ABC,
,
,
,点D,E分别在棱
和棱
上,且
,
,M为棱
的中点.
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8bfe2553e852df73185d017c0a62fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209acf15985d1ea1ad86fc4a37e38c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8cb98c0adee7ca698d8b17dacb845b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a0268d04b9dea7629af27af9a0285a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8973bcb7d87303a0b5fba04a801019b9.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/537b25d7d8d13a6ef990c7c370def871.png)
您最近一年使用:0次
2022-06-10更新
|
1518次组卷
|
8卷引用:广西2023届高三上学期开学摸底考试数学(文)试题
广西2023届高三上学期开学摸底考试数学(文)试题广西柳州市鹿寨县鹿寨中学2023届高三上学期开学摸底考试数学(文)试题黑龙江省哈尔滨市第九中学校2022届高三第三次模拟考试数学(文科)试题(已下线)专题31 直线、平面垂直的判定与性质-1内蒙古赤峰市2021-2022学年高一下学期期末考试数学(文)试题(已下线)8.6.2 直线与平面垂直(1) -2022-2023学年高一数学《考点·题型·技巧》精讲与精练高分突破系列(人教A版2019必修第二册)(已下线)第06讲 空间直线﹑平面的垂直(一)-《知识解读·题型专练》(已下线)第十一章:立体几何初步章末重点题型复习(2)-同步精品课堂(人教B版2019必修第四册)