1 . 如图,四棱锥
的底面是矩形,
底面
为
的中点,且
.
![](https://img.xkw.com/dksih/QBM/2021/11/7/2846338308415488/2849570917261312/STEM/601cd32e2e864e8d8df57396769b3f7f.png?resizew=159)
(1)证明:平面
平面
;
(2)若
,求四棱锥
的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfaefb10f82b89802bb420b3c41de1bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186e5e7efe51fd25b9e38dc0fa23de9d.png)
![](https://img.xkw.com/dksih/QBM/2021/11/7/2846338308415488/2849570917261312/STEM/601cd32e2e864e8d8df57396769b3f7f.png?resizew=159)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392469b357b12b998528499929366c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40d4d36ae30487030b827ce9413b9f13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
2021-11-12更新
|
1040次组卷
|
4卷引用: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)
(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)(已下线)专题2 空间几何体的面积运算(基础版)云南大理、丽江、怒江2022届高三第一次复习统一检测数学(文)试题专题6.4 空间中的垂直关系-2021-2022学年高一数学北师大版2019必修第二册
名校
解题方法
2 . 已知圆锥
的底面半径为2,母线长为
,点C为圆锥底面圆周上的一点,O为圆心,D是
的中点,且
.
![](https://img.xkw.com/dksih/QBM/2021/10/7/2824292656529408/2829353448177664/STEM/58b3b4f050aa4d24b772ae98f50f9ef1.png?resizew=200)
(1)求三棱锥
的表面积;
(2)求A到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60cbb271baca5cd015f30e07d9eebfd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b895d317c1f6a38bb2337ab6e4803008.png)
![](https://img.xkw.com/dksih/QBM/2021/10/7/2824292656529408/2829353448177664/STEM/58b3b4f050aa4d24b772ae98f50f9ef1.png?resizew=200)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a83765b08477282f437dca37863cf54.png)
(2)求A到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3201d3796ed9a29338aac25245a7c8e2.png)
您最近一年使用:0次
2021-10-14更新
|
871次组卷
|
6卷引用:考向22 空间几何体-备战2022年高考数学一轮复习考点微专题(上海专用)
(已下线)考向22 空间几何体-备战2022年高考数学一轮复习考点微专题(上海专用)(已下线)专题1 空间几何体-学会解题之高三数学321训练体系【2022版】(已下线)考点16 空间几何体-2-(核心考点讲与练)-2023年高考数学一轮复习核心考点讲与练(新高考专用)上海市2022届高三上学期一模暨春考模拟卷(二)数学试题广东省中山市2022届高三上学期期末数学试题河北省衡水市第二中学2023-2024学年高二上学期学科素养评估(三调)数学试题
解题方法
3 . 如图所示,圆形纸片的圆心为
,半径为
,该纸片上的等边三角形
的中心为
,点
,
,
为圆
上的点,
分别是以
为底边的等腰三角形,沿虚线剪开后,分别以
为折痕折起
,使得
,
,
重合,得到三棱锥,则当
的边长变化时,求三棱锥的表面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ec556703fc98d32003759064c20b14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d371059f22172ea523630040a5a9cb9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/746ee1515a178948b04f535705c6f738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/746ee1515a178948b04f535705c6f738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d371059f22172ea523630040a5a9cb9e.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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://img.xkw.com/dksih/QBM/2021/12/2/2863855434399744/2867481866919936/STEM/a34cc19e3ccc4ec9b0198205648083ea.png?resizew=207)
您最近一年使用:0次
2021-12-07更新
|
553次组卷
|
6卷引用:第1讲 空间几何体的表面积与体积(练)-2022年高考数学二轮复习讲练测(新教材地区专用)
(已下线)第1讲 空间几何体的表面积与体积(练)-2022年高考数学二轮复习讲练测(新教材地区专用)(已下线)高一数学下学期期中精选50题(提升版)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)(原卷版)(已下线)8.3 简单几何体的表面积与体积安徽省滁州市定远县育才学校2021-2022学年高一下学期第一次月考数学试题河北省衡水市冀州区第一中学2020-2021学年高一下学期期中数学试题(已下线)8.3简单几何体的表面积与体积A卷
名校
解题方法
4 . 如图,已知四棱锥
的底面
是边长为2的正方形,
面
.
![](https://img.xkw.com/dksih/QBM/2021/11/28/2860787536486400/2861286731759616/STEM/803c6022-4309-494f-8053-bf9f535a8a93.png?resizew=273)
(1)求证:面
面
;
(2)求四棱锥
的侧面积.
![](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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de4c27f9ef3b9cc6899065cf4ef001e.png)
![](https://img.xkw.com/dksih/QBM/2021/11/28/2860787536486400/2861286731759616/STEM/803c6022-4309-494f-8053-bf9f535a8a93.png?resizew=273)
(1)求证:面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
名校
解题方法
5 . 如图,三棱锥
中,
,
,
两两垂直,
,
,
分别是
,
的中点,
的面积为
,四棱锥
的体积为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/18786fc0-1e66-480d-a19f-9a9d914146b6.png?resizew=170)
(1)若平面
平面
,求证:
;
(2)求三棱锥
的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3304e23f3b0f9569c4140ca89b6498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75764c506b7ff847a7960ed28371f49b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/18786fc0-1e66-480d-a19f-9a9d914146b6.png?resizew=170)
(1)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd82d880985b1490bc5f4bb7fdee1cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baceb049bf16ed0fd33639fdda0ec5ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3237c82088b1ac0c5ba31b7714d5164b.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
您最近一年使用:0次
2021-10-15更新
|
2346次组卷
|
5卷引用:第03讲 空间直线、平面的平行 (精讲)-1
(已下线)第03讲 空间直线、平面的平行 (精讲)-1吉林省双辽市一中、大安市一中、通榆县一中等重点高中2021-2022学年高三上学期期末联考数学(文)试题江西省上饶市重点高中2022-2023学年高二上学期开学考试数学试题河南省联考2021-2022学年高三核心模拟卷(上)文科数学(四)(已下线)四川省成都市双流区双流棠湖中学2023-2024学年高二上学期期中数学试题
解题方法
6 . 如图,在三棱锥
中,
平面
,
,
与
的长度之和为6米,
,现要给三棱锥
的侧面刷油漆,每平方米需要0.5升油漆,油漆价格为60元/升.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/f5a10479-88be-4b00-bd8a-e44b10b33352.png?resizew=198)
(1)设
米,三棱锥
的侧面共需要油漆
升,试写出
关于
的函数表达式;
(2)刷油漆需要请油漆工来完成,工费按照每平方米10元计算,若油漆工工费及油漆费用的总预算为400元,试问最后油漆工工费及油漆费用是否有可能会超预算?说明你的理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf9718967af7a01c5b4866ea6f73bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bfa3242965ce027bbef9168bfb73b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf9718967af7a01c5b4866ea6f73bbb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/f5a10479-88be-4b00-bd8a-e44b10b33352.png?resizew=198)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c7a3d679b4dae63575903387a76ce45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf9718967af7a01c5b4866ea6f73bbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)刷油漆需要请油漆工来完成,工费按照每平方米10元计算,若油漆工工费及油漆费用的总预算为400元,试问最后油漆工工费及油漆费用是否有可能会超预算?说明你的理由.
您最近一年使用:0次
2021-10-12更新
|
403次组卷
|
4卷引用:专题1 空间几何体-学会解题之高三数学321训练体系【2022版】
(已下线)专题1 空间几何体-学会解题之高三数学321训练体系【2022版】(已下线)考点16 空间几何体-2-(核心考点讲与练)-2023年高考数学一轮复习核心考点讲与练(新高考专用)湖北省金太阳百校联考2021-2022学年高三上学期10月月考数学试题辽宁省葫芦岛市协作校2021-2022学年高三上学期第一次考试数学试题
名校
解题方法
7 . 如图,在底面为矩形的四棱锥
中,
为棱
上一点,
底面
.
![](https://img.xkw.com/dksih/QBM/2021/9/5/2801457050214400/2803622616465408/STEM/e2b71e7bfc884c168a81448c0fb7324c.png?resizew=206)
(1)证明:
;
(2)若
,
,过
作
平面
,垂足为
,求三棱锥
的侧面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/db807b09cc550f476b3f8fa0c6a14425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/2021/9/5/2801457050214400/2803622616465408/STEM/e2b71e7bfc884c168a81448c0fb7324c.png?resizew=206)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c583493109d50c9e4634c05e9042a9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30b0393ce62b24aa5f9b740d4cc6743b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d8d147b8943cbd5ea5337be5627b3f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630cbaf628064c66436caa267201bc55.png)
您最近一年使用:0次
2021-09-08更新
|
174次组卷
|
3卷引用: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)
(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)甘肃省白银市靖远县2021-2022学年高三上学期开学考试数学(文科)试题青海省海南州中学2021-2022学年高二上学期第一次月考数学(文)试题
名校
8 . 在四棱锥
中,底面
是正方形,
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/5/7/2715986552438784/2794686000177152/STEM/68e72234-67af-44f7-8d52-b7aa81a8a350.png?resizew=177)
(1)分别取侧棱
、
中点
、
,证明:直线
与平面
平行;
(2)求四棱锥
的表面积.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://img.xkw.com/dksih/QBM/2021/5/7/2715986552438784/2794686000177152/STEM/68e72234-67af-44f7-8d52-b7aa81a8a350.png?resizew=177)
(1)分别取侧棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
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2021-08-26更新
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4卷引用:第04讲线线、线面、面面平行的判定与性质(核心考点讲与练)(3)
(已下线)第04讲线线、线面、面面平行的判定与性质(核心考点讲与练)(3)上海市徐汇中学2022-2023学年高二上学期期中数学试题上海市建平中学2020-2021学年高二下学期期中数学试题江西省遂川中学2021-2022学年高二上学期第二次月考数学(理)试题(B卷)
名校
9 . 正棱锥S﹣ABCD的底面边长为4,高为1.
(2)棱锥的表面积与体积.
(2)棱锥的表面积与体积.
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2021-07-24更新
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907次组卷
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7卷引用:第08讲 简单几何体的表面积和体积(核心考点讲与练)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)
(已下线)第08讲 简单几何体的表面积和体积(核心考点讲与练)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)沪教版(2020) 必修第三册 新课改一课一练 第11章 单元复习辽宁省六校协作体2021-2022学年高一下学期第三次联合考试数学试题(已下线)期中测试卷01--《重难点题型·高分突破》(人教A版2019必修第二册)黑龙江省鹤岗市第一中学2020-2021学年高一下学期期末数学试题广东省肇庆市封开县广信中学等几校2022-2023学年高一下学期期中联考数学试题吉林省普通高中友好学校联合体2023-2024学年高一下学期期中考试数学试卷
20-21高三下·浙江·期末
解题方法
10 . 如图,正四棱锥
中,
,
,E为
中点.
![](https://img.xkw.com/dksih/QBM/2021/5/29/2731412325097472/2731585620705280/STEM/db6b0df4b2d74e83aa6d4b1645e5ae86.png?resizew=163)
(1)求证:
平面
;
(2)求异面直线
与
所成角的余弦值;
(3)求三棱锥
的表面积和体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87a0b15556a1584c1b6b2768bbc9cbda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
![](https://img.xkw.com/dksih/QBM/2021/5/29/2731412325097472/2731585620705280/STEM/db6b0df4b2d74e83aa6d4b1645e5ae86.png?resizew=163)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1ea0adc03fc8ba355dbdac586f4b707.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42020cfacd62b300cad053981bab9e0b.png)
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