解题方法
1 . 如图,在四棱锥
中,底面ABCD是矩形,
底面ABCD,且
,
,
,E,F分别是PC,BD的中点.
平面PAD;
(2)再从条件①、条件②、条件③这三个条件中选择一个作为已知,求三棱锥
的体积.
条件①:G是棱BC上一点,且
;
条件②:G是PB的中点;
条件③:G是
的内心(内切圆圆心).
注;如果选择多个条件分别解答,按第一个解答计分.
![](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/1bec03e804f0cea1db5cde2aa185056a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
(2)再从条件①、条件②、条件③这三个条件中选择一个作为已知,求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c91c147bac6c7b670992b5e3ada94b72.png)
条件①:G是棱BC上一点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa0d8cc5869cc7e551dd4e204c58ec68.png)
条件②:G是PB的中点;
条件③:G是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
注;如果选择多个条件分别解答,按第一个解答计分.
您最近一年使用:0次
2023-07-10更新
|
374次组卷
|
5卷引用:北京市通州区2022-2023学年高一下学期期末质量检测数学试题
北京市通州区2022-2023学年高一下学期期末质量检测数学试题【北京专用】专题12立体几何与空间向量(第一部分)-高一下学期名校期末好题汇编(已下线)模块二 专题4 立体几何中的平行与垂直的位置关系 能力卷B(已下线)模块二 专题7 立体几何中的平行与垂直的位置关系 能力卷B(已下线)专题06 空间中点线面的位置关系6种常考题型归类(1)-期期末真题分类汇编(北京专用)
名校
2 . 在正四棱柱
中,
,M是
的中点.
(1)证明:
平面
.
(2)若正四棱柱的表面积是10,求该正四棱柱的外接球的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/17/efb386bc-36cb-49e0-b304-94795f1af3c0.png?resizew=115)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f11f1840eb8b17e7b07c3fe7e987a9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb304d905125170bebfada27e7ed8960.png)
(2)若正四棱柱的表面积是10,求该正四棱柱的外接球的体积.
您最近一年使用:0次
3 . 如图是一个正四棱台
的石料,上、下底面的边长分别为
和
,高
.
的表面积;
(2)若要这块石料最大限度打磨为一个圆台,求圆台
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe9f7abf7bcf4e1aa2579cd191d7761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e57171806f407a98dd8a796d4d2d6bbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3668a3f3ce5b8a272ad92c2ebd233f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
(2)若要这块石料最大限度打磨为一个圆台,求圆台
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b851898d01cc1b4bf3275b475245c46.png)
您最近一年使用:0次
2023-05-20更新
|
1324次组卷
|
3卷引用:北京市东城区北京景山中学2022-2023学年高一下学期期中考试数学试题
名校
4 . 无数次借着你的光,看到未曾见过的世界:国庆七十周年、建党百年天安门广场三千人合唱的磅礴震撼,“930烈士纪念日”向人民英雄敬献花篮仪式的凝重庄严
金帆合唱团,这绝不是一个抽象的名字,而是艰辛与光耀的延展,当你想起他,应是四季人间,应是繁星璀璨!这是开学典礼中,我校金帆合唱团的颁奖词,听后让人热血沸腾,让人心向往之.图1就是金帆排练厅,大家都亲切的称之为“六角楼”,其造型别致,可以理解为一个正六棱柱(图2)由上底面各棱向内切割为正六棱台(图3),正六棱柱的侧棱
交
的延长线于点
,经测量
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9edf5b5d5de0dc8433f8e49b93d79e7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/13/dae99132-bfad-4b9d-b1fe-601d36cad5e6.png?resizew=150)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/13/8eeda22d-adba-4dfe-b56f-c8331e954444.png?resizew=163)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/13/40498824-4beb-4838-b919-a133b83c7ecb.png?resizew=191)
(1)写出三条正六棱台的结构特征.
(2)“六角楼”一楼为办公区域,二楼为金帆排练厅,假设排练厅地板恰好为六棱柱中截面,忽略墙壁厚度,估算金帆排练厅对应几何体体积.(棱台体积公式:
)
(3)“小迷糊”站在“六角楼”下,陶醉在歌声里.“大聪明”走过来说:“数学是理性的音乐,音乐是感性的数学.学好数学方能更好的欣赏音乐,比如咱们刚刚听到的一个复合音就可以表示为函数
,你看这多美妙!”
“小迷糊”:“.....”
亲爱的同学们,快来帮“小迷糊”求一下
的最大值吧.
注:可以参考(不限于)下面公式:
①
元均值不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faa52b46f115de52814795d65da5238f.png)
②琴生不等式:
若函数
在
上为“凸函数”,且
为
上任意
个实数,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1821e1ae466356718b3fc4e616fb8503.png)
注:
在
是“凸函数”
③柯西不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c54ff21406dc68cdab0d21351daf51.png)
注:其二元形式为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eece548f90ab9654e1dd55340431f4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e4fa04825ac7d071968056322d88be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f92a8ba0b29a1e1eca637c01b7f39b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9edf5b5d5de0dc8433f8e49b93d79e7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/13/dae99132-bfad-4b9d-b1fe-601d36cad5e6.png?resizew=150)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/13/8eeda22d-adba-4dfe-b56f-c8331e954444.png?resizew=163)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/13/40498824-4beb-4838-b919-a133b83c7ecb.png?resizew=191)
(1)写出三条正六棱台的结构特征.
(2)“六角楼”一楼为办公区域,二楼为金帆排练厅,假设排练厅地板恰好为六棱柱中截面,忽略墙壁厚度,估算金帆排练厅对应几何体体积.(棱台体积公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7850942557a95467b4159b86c1f25678.png)
(3)“小迷糊”站在“六角楼”下,陶醉在歌声里.“大聪明”走过来说:“数学是理性的音乐,音乐是感性的数学.学好数学方能更好的欣赏音乐,比如咱们刚刚听到的一个复合音就可以表示为函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3387b0d9e635720bbbe3fe28b536200.png)
“小迷糊”:“.....”
亲爱的同学们,快来帮“小迷糊”求一下
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3888740fa8b552b55b4a0c8ae4166007.png)
注:可以参考(不限于)下面公式:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faa52b46f115de52814795d65da5238f.png)
②琴生不等式:
若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe1c31a81f198c443e71b83ca662939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4562f3225c98cf5cb11b47d98c9cc9c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1821e1ae466356718b3fc4e616fb8503.png)
注:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3162d2c7b650bba3e401ffbb1e13bb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ff8dca35b759d3051b62badd7d76bc.png)
③柯西不等式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c54ff21406dc68cdab0d21351daf51.png)
注:其二元形式为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d115a39e93fabee911c86269199e13d0.png)
您最近一年使用:0次
5 . 如图,在直角梯形ABCD中,AB∥DC,∠BAD=90°,AB=4,AD=2,DC=3,点E在CD上,且DE=2,将△ADE沿AE折起,使得平面ADE⊥平面ABCE,G为AE中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/26/7e2b4cfc-f4d4-48ec-b5bd-21fcd78288f8.png?resizew=439)
(1)求证:DG⊥平面ABCE;
(2)求四棱锥D-ABCE的体积;
(3)在线段BD上是否存在点P,使得CP∥平面ADE?若存在,求
的值;若不存在,请说明理由.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/26/7e2b4cfc-f4d4-48ec-b5bd-21fcd78288f8.png?resizew=439)
(1)求证:DG⊥平面ABCE;
(2)求四棱锥D-ABCE的体积;
(3)在线段BD上是否存在点P,使得CP∥平面ADE?若存在,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/747978ec67fee6ee9eb07d02b80987d7.png)
您最近一年使用:0次
解题方法
6 . 在正方体
中,
是棱
上异于顶点的动点.
(1)用斜二测画法作出正方体及过
三点的截面的图形,直接写出该截面图形的形状;
(2)若
是棱
的中点,求正方体被(1)中的截面所截得两个几何体的体积之比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
(1)用斜二测画法作出正方体及过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cda66f976efa629a8f0f517e2efc417.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
您最近一年使用:0次
解题方法
7 . 一个圆锥的底面半径为
,高为
,在其内部有一个高为
的内接圆柱.
(1)求圆锥的侧面积和体积;
(2)当
为何值时,圆柱的侧面积最大?并求出侧面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c78d0ab561d0c9bb9099772c596af8bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd6f4250ca6b1b9bce234a01f00d44d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3160fce05b551569b8c7b5de6dd8b6.png)
(1)求圆锥的侧面积和体积;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
8 . 我们知道,二元实数对
可以表示平面直角坐标系中点的坐标; 那么对于
元实数对![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a79b7ec77425af9152ef0cd3dacfe9.png)
,
是整数
,也可以把它看作一个由
条两两垂直的“轴”构成的高维空间(一般记为
中的一个“点”的坐标表示的距离
.
(1)当
时, 若
,
,
, 求
,
和
的值;
(2)对于给定的正整数
,证明
中任意三点
满足关系
;
(3)当
时,设
,
,
,其中
,
,
,
.求满足
点的个数
,并证明从这
个点中任取11个点,其中必存在
个点,它们共面或者以它们为顶点的三棱锥体积不大于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60a79b7ec77425af9152ef0cd3dacfe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf1c689bacb131759ccd37e444a9479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/837d6c4f226776680f464ae63f90a845.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80ebc8c7e32c1b561a908a36cfa2cbb5.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc2d3df37e73a8abea815f37dbb3fff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/115a0c87ac14dbb770c95d74d6e26073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/567fc6dde8cea2eccafe83048ed9b650.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/445fa8fa15fbb33d26fff11f18113cfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3bcb4828b16c8e845492f1a53ddd9a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cdfd65ee99c3d93adee6732ae125eb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1740273d1682d06d35e35a733225613d.png)
(2)对于给定的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93de25834c572256e25333010fbda97b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1898f935cafa18dc3e7ea4cea8b46df.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be604061cf1591f7069472269d4c9719.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a42bc893aeabafad84da3e66e73f885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58dcb69f052798e9238906eb18031a0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b82ad92798b264062c062f4a9a1a5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72551dcd7eb2722ee2ef5f5054a751e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c7135c6c4b5aa75a8efa8171dbba42b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a391005600bdd69c96750589f9adb048.png)
您最近一年使用:0次
21-22高一下·北京·期末
解题方法
9 . 如图, 在三棱锥
中,已知
是正三角形,
平面
,
,
为
的中点,
在棱
上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/3/ab06d698-66d5-46fe-a2e4-642d5fabaf5e.png?resizew=212)
(1)求三棱锥
的体积;
(2)求证:
平面
;
(3)若
为
中点, 是否存在
在棱
上,
,且
平面
? 若存在,求
的值并说明理由;若不存在,给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d150134e5018f74fc4e8a016ced5f11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/457eb716c608c6b4fb6e91c8fc2ed163.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/3/ab06d698-66d5-46fe-a2e4-642d5fabaf5e.png?resizew=212)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18da88f27cc36dbf1d01bcea7341bc37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf5909a2b109d048bd7c7a0377a769f.png)
您最近一年使用:0次
10 . 如图,已知正方体
的棱长为
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/2022/7/16/3023977212796928/3026767498633216/STEM/10c1f5963af74939800e1197a3111cdc.png?resizew=206)
(1)求证:平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
平面
;
(2)求证:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
平面
;
(3)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd110e5d9ab042968ec706b44e78572.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b30b4f9feb6c37052d200b9f46c6a66.png)
![](https://img.xkw.com/dksih/QBM/2022/7/16/3023977212796928/3026767498633216/STEM/10c1f5963af74939800e1197a3111cdc.png?resizew=206)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86eec8526479272d15bb3b171a46de0.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b54387f870ae37f7951b253665d64f6.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eafde3cd0e1c6c3d09706aa0f728afa.png)
您最近一年使用:0次