1 . 如图,在三棱柱
中,
.
平面
;
(2)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ee282fe2fb0954b12fbc1bea093b66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21dee56b9f36ba8f76fe67b76383636b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8da5a89f5938fe9ac2f86aab28e334dc.png)
您最近一年使用:0次
名校
解题方法
2 . 正四棱锥
中,
,
,其中
为底面中心,
为
上靠近
的三等分点.
平面
;
(2)求四面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764829cc2c763b6aca0665aa143e304e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df5935c893580c77ab6fa6eb0a70bdb.png)
(2)求四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0242f1d6a2dd3c0d14961339164e298.png)
您最近一年使用:0次
2023-11-13更新
|
1231次组卷
|
10卷引用:青海省西宁市2024届高三上学期期末联考数学(文)试题
青海省西宁市2024届高三上学期期末联考数学(文)试题青海省西宁市海湖中学2023-2024学年高二下学期开学考试数学试卷上海市文来中学2024届高三上学期期中数学试题(已下线)考点9 垂直的判定与性质 2024届高考数学考点总动员四川省南充市阆中中学校2024届高三一模数学(文)试题西藏自治区拉萨市部分学校2023-2024学年高二上学期期末联考数学(理)试题(已下线)模块三 专题4 大题分类练(立体几何)基础夯实练新疆维吾尔自治区喀什地区喀什十四校2023-2024学年高二上学期期末数学试题(已下线)第12讲 8.6.2直线与平面垂直的判定定理(第1课时)-【帮课堂】(人教A版2019必修第二册)(已下线)重难点专题10 轻松解决空间几何体的体积问题-【帮课堂】(苏教版2019必修第二册)
3 . 如图,在三棱锥
中,
底面
,
,
,
分别是
的中点.
(1)求证:
平面
;
(2)求四面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6deecf9ccb7b7879455050633219e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8e24b38eb08a9d9f76be5719c822fb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46750bbbe806863d5d70c8f4eaf6942.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/22/91c7b59c-2cb6-4817-a3b4-29007b92612f.png?resizew=115)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b78172568aac9805d2ea2d5f742bf80c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc6f6dfdbe7d39891c35f67e1a95c7f.png)
(2)求四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
您最近一年使用:0次
2023-08-20更新
|
144次组卷
|
2卷引用:青海省海南藏族自治州高级中学2022-2023学年高一下学期期中考试数学试题
解题方法
4 . 如图所示,在直三棱柱
中,
分别为棱
的中点,
.
平面
;
(2)求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf59cb1a46939789493e067f21ea1b77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9debd13454918684cf8e07ce210516fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f868db591e0e98d5ec027f3388aecca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063510e3c1fb6a7ccc3b8e3e3c7d660e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
(2)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2686c1c5758fc36e7417f7c8e2a9d8b7.png)
您最近一年使用:0次
2023-09-30更新
|
729次组卷
|
3卷引用:青海省西宁市大通县2024届高三上学期开学摸底考试数学(文科)试题
青海省西宁市大通县2024届高三上学期开学摸底考试数学(文科)试题8.5.2直线与平面平行练习(已下线)专题18 直线与直线平行 直线与平面平行-《重难点题型·高分突破》(人教A版2019必修第二册)
名校
解题方法
5 . 如图,四棱锥
中,底面
是边长为
的正方形,
是
的中心,
底面
,
是
的中点.
(1)求证:
平面
;
(2)若
,求三棱锥
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/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/21/888665b4-0c89-485a-99d8-2534ffce9190.png?resizew=182)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/954c584f9c868d235e0fc1debb14428d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07445aa3909818a3ef93bb01182f545f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42020cfacd62b300cad053981bab9e0b.png)
您最近一年使用:0次
2023-08-20更新
|
1401次组卷
|
6卷引用:青海省西宁北外附属新华联外国语高级中学2023-2024学年高三上学期第一次月考数学试题
解题方法
6 . 如图,在三棱柱
中,
为边长为
的正三角形,
为
的中点,
,且
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/dcd0f718-5735-4e7a-b235-9a8883df44aa.png?resizew=195)
(1)证明:
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be445f94888b34161b6d59d458928e35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50d9bdbbdfabc737323692c796e41930.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/dcd0f718-5735-4e7a-b235-9a8883df44aa.png?resizew=195)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/005c110169a6aa55414175b8e76fc9da.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed27ea773e11865b0dd40c54822a7e26.png)
您最近一年使用:0次
2023-02-19更新
|
1089次组卷
|
5卷引用:青海省西宁市大通回族土族自治县2022-2023学年高三下学期开学摸底考试数学(文)试题
青海省西宁市大通回族土族自治县2022-2023学年高三下学期开学摸底考试数学(文)试题(已下线)第八章立体几何初步(综合检测卷)(已下线)8.6.3 平面与平面垂直(分层作业)-【上好课】2022-2023学年高一数学同步备课系列(人教A版2019必修第二册)(已下线)8.6.3 平面与平面垂直(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)专题8.13 空间直线、平面的垂直(二)(重难点题型精讲)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)
7 . 如图,
是圆锥的顶点,
是底面圆心,
是底面圆的一条直径,且点
是弧
的中点,点
是
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/14/bc4dc791-7b45-4168-a52c-01bc3c4d1866.png?resizew=172)
(1)求圆锥的表面积;
(2)求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4556f395fc12b293fc6c469c861791fd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/14/bc4dc791-7b45-4168-a52c-01bc3c4d1866.png?resizew=172)
(1)求圆锥的表面积;
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11477bf45c2ad9d554d8f2dbacb5bb67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c49e7453a0a54f1fc47391320cd95db9.png)
您最近一年使用:0次
8 . 如图,在四棱柱
中,四边形ABCD是正方形,E,F,G分别是棱
,
,
的中点.
![](https://img.xkw.com/dksih/QBM/2022/6/1/2991817753714688/2996335044198400/STEM/71f0f333-de44-4b84-b7cf-b3da87528b37.png?resizew=227)
(1)证明:平面
平面
;
(2)若点
在底面ABCD的投影是四边形ABCD的中心,
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/2022/6/1/2991817753714688/2996335044198400/STEM/71f0f333-de44-4b84-b7cf-b3da87528b37.png?resizew=227)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad4cbffc6d58be7ec916912b632ae58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d4b75674b3bd22476b307419d4476b2.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11b67f63997d21064d9c52494bd57d16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7cfd72e190f8affc92d8d2a11068a6.png)
您最近一年使用:0次
2022-06-07更新
|
1212次组卷
|
5卷引用:青海省西宁北外附属新华联外国语高级中学2022-2023学年高三上学期期末考试数学(文)试题
青海省西宁北外附属新华联外国语高级中学2022-2023学年高三上学期期末考试数学(文)试题河南省部分学校2022届高三下学期5月考前最后一卷文科数学试题(已下线)专题22 空间中的平行关系(针对训练)-2023年高考数学一轮复习精讲精练宝典(新高考专用)(已下线)第03讲 空间直线、平面的平行 (精讲)-2(已下线)8.5.3 平面与平面平行 (精讲)(2)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)
解题方法
9 . 如图,四边形
为正方形,E,F分别为
和
的中点,以
为折痕把
折起,使点C到达点P的位置,且
平面
.
![](https://img.xkw.com/dksih/QBM/2022/1/12/2893081990422528/2909858442321920/STEM/38fedb11-1ca8-4591-900b-72cb58af0d0f.png?resizew=226)
(1)证明:
;
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d004d2d115b477ade6af7ddb93db0df8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a37ba261860ddad9d11b2e8348a8f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f020ca4ad44801691235958e253907d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85719346f464a101d365d42be27450a3.png)
![](https://img.xkw.com/dksih/QBM/2022/1/12/2893081990422528/2909858442321920/STEM/38fedb11-1ca8-4591-900b-72cb58af0d0f.png?resizew=226)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5621416de1b6b5e4418d35f2e23daea1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abb4114ae425d31ea6b554b328163a14.png)
您最近一年使用:0次
2022-02-05更新
|
379次组卷
|
2卷引用:青海省西宁市大通县2024届高三上学期期中数学(文)试题
名校
解题方法
10 . 三棱锥
中,平面
平面
,
为等边三角形,
且
,
、
分别为
、
的中点.
平面
;
(2)求证:平面
平面
;
(3)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a94d59dee2d5a8f0425b64b2083825.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8704811c9c5dba854310ae0de2ba6b05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7eaac66c8a1d94860390668ffecfaba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19bc7774144c164f7ebaeca54fa657e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4fce8e923062b9779553d6f282895b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eed6757a4ff7cd9042c4078bd910583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08452588675f76da2f8d31387b3a8224.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90cacdef2c5f2a4b00a1f4f3fe77bd9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f526e2fe627bb4ddebe708c07d0a22fc.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a94d59dee2d5a8f0425b64b2083825.png)
您最近一年使用:0次
2021-04-02更新
|
2536次组卷
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19卷引用:青海省西宁市第十四中学2019-2020学年高二上学期期末数学(文)试题
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