名校
1 . 如图,在四棱锥
中,底面ABCD为正方形,
平面ABCD,M,N分别为棱PD,BC的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/15/3a438676-f6ad-42ec-a05b-416826f1dff2.png?resizew=141)
(1)求证:
平面PAB;
(2)求直线MN与平面PBD所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/15/3a438676-f6ad-42ec-a05b-416826f1dff2.png?resizew=141)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
(2)求直线MN与平面PBD所成角的正弦值.
您最近一年使用:0次
2023-05-14更新
|
747次组卷
|
4卷引用:四川省广元中学2022-2023学年高二下学期期中数学试题(文科)
名校
解题方法
2 . 如图,在三棱锥
中,平面
平面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/7/26/2772274677424128/2774663640260608/STEM/3f734ec70364442380cc69b65e4b385b.png?resizew=244)
(1)求证
;
(2)求四面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddfe0ccf24d760c77535a70c92dad145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0423c674207216397dde032c17816696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077c956ac0eb05cf120e14f17413dfa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e66cef506a91c5e28723f6f19895c27b.png)
![](https://img.xkw.com/dksih/QBM/2021/7/26/2772274677424128/2774663640260608/STEM/3f734ec70364442380cc69b65e4b385b.png?resizew=244)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5ea309886e947ea7cb4b81716206fd.png)
(2)求四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da6d7e887348f80fda1e157e0222573d.png)
您最近一年使用:0次
2021-07-29更新
|
235次组卷
|
2卷引用:四川省广元市2020-2021学年高二下学期期末数学(文科)试题
解题方法
3 . 如图,在矩形
中,
,
为边
的中点,以
为折痕把
折起,使点
到达点
的位置,且使平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/509b4245-a300-487e-a522-157cc0cc24d3.png?resizew=249)
(1)证明:
;
(2)求三棱锥
的体积.
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c3c8bf858c13b295de56e548116db9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c505f9d4513028bb16e274aae96cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/509b4245-a300-487e-a522-157cc0cc24d3.png?resizew=249)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaef9e92d148afff22761d5e027d3ee.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec13727470aa1196755308d6232abfc.png)
您最近一年使用:0次
2020-06-14更新
|
431次组卷
|
2卷引用:四川省广元市高2020届第三次高考适应性统考数学(文科)试题
4 . 如图所示,正三棱柱ABC-A1B1C1的高为2,点D是A1B的中点,点E是B1C1的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/761379a9-3a4b-4775-a320-f43646932b7a.png?resizew=179)
(1)证明:DE∥平面ACC1A1;
(2)若三棱锥E-DBC的体积为
,求该正三棱柱的底面边长.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/761379a9-3a4b-4775-a320-f43646932b7a.png?resizew=179)
(1)证明:DE∥平面ACC1A1;
(2)若三棱锥E-DBC的体积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da11ecd491d67cc6cdc4f5421bf6f149.png)
您最近一年使用:0次
2019-12-16更新
|
1396次组卷
|
7卷引用:【市级联考】四川省广元市高三2019届第一次高考适应性统考数学试题
5 . 如图,在斜三棱柱
中,已知
,
,且
.
![](https://img.xkw.com/dksih/QBM/2018/7/24/1995250739593216/2020756539613184/STEM/31d98bcfc3614232943b6d36192b0037.png?resizew=187)
(Ⅰ)求证:平面
平面
;
(Ⅱ)若
,求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcfdaff6c0ebc150c81ce52a0cb95469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2e5dc81fbafbe58bff0842f7776d80a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46fe926770d2354e172dec02f5ce2efe.png)
![](https://img.xkw.com/dksih/QBM/2018/7/24/1995250739593216/2020756539613184/STEM/31d98bcfc3614232943b6d36192b0037.png?resizew=187)
(Ⅰ)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cdaadeae37736a1e6dd93fa1fe712f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
(Ⅱ)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e448cf106f584695cce0ae1fdc16f9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c61e6d34503a713684bb25be96edbcd.png)
您最近一年使用:0次
2018-08-29更新
|
2117次组卷
|
4卷引用:2019届四川省广元市高三第二次高考适应性统考数学文试题
2019届四川省广元市高三第二次高考适应性统考数学文试题【市级联考】江西省南昌市2017-2018学年度高三第二轮复习测试卷文科数学(一)试题甘肃省师大附中2019届高三上学期期中模拟文科数学试卷(已下线)2019届神州智达高三诊断性大联考(三)文科数学(预测卷Ⅰ)
6 . 如图,
是以
为直角的三角形,
平面
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/e618330c-c02c-46b8-87fb-7161e51f1ff6.png?resizew=147)
(1)求证:
;
(2)
为线段
上的点,当二面角
的余弦值为
时,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10c83f8945042b9c8fb2fbdac9308d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47550fcb04c9bf3a0782784fd8c7a632.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5480072a61b457c202dc51f8c5ee4478.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/e618330c-c02c-46b8-87fb-7161e51f1ff6.png?resizew=147)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f479d987bc7abd828c64f9dc745836ab.png)
(2)
![](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/d4addd1eda028fa61d4731e27b6f8b86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64f1145c162038df3c7184d9201c628e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/994f9f397699534639e9a2c9bacaad44.png)
您最近一年使用:0次
7 . 如图四棱锥
,底面梯形
中,
,平面
平面
,已知
.
(1)求证:
;
(2)线段
上是否存在点
,使三棱锥
体积为三棱锥
体积的6倍.若存在,找出点
的位置;若不存在,说明理由.
![](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/68d31600cba2d5256c7e78b6122d6755.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/49d382b96f2d761ec5347cbf912c1e6a.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/712f7375b4ede5f75c0d81870c0f86af.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddfe0ccf24d760c77535a70c92dad145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e76f6552e20faeba98588e9b5dd01f6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/2018/1/11/1857880339120128/1858907873681408/STEM/78541ac226584d888a166234de03e269.png?resizew=222)
您最近一年使用:0次
2018-01-12更新
|
385次组卷
|
4卷引用:四川省广元市2018届高三第一次高考适应性统考(文科)数学试题
四川省广元市2018届高三第一次高考适应性统考(文科)数学试题(已下线)2018年高考二轮复习测试专项【新课标文科】热点八 几何体的表面积与体积的求解(已下线)2018年高考二轮复习测试专项【新课标理科】热点八 几何体的表面积与体积的求解2020年普通高等学校招生全国统一考试 文科数学样卷(六)
8 . 如图,四边形
是梯形.四边形
是矩形.且平面
平面
,
,
,
是线段
上的动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/13/d1645432-6fd1-4728-9f19-7f569fec9348.png?resizew=243)
(1)试确定点
的位置,使
平面
,并说明理由;
(2)在(1)的条件下,且
,
,
,连接
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32c05247f6998d7a70d31d13be4148c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97e45b6f8cf0260912f587c04f9f2442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/13/d1645432-6fd1-4728-9f19-7f569fec9348.png?resizew=243)
(1)试确定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f81fa367ec317fe2a30142e1c30cce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66058ff40f4ebfc19490eb4e20360752.png)
(2)在(1)的条件下,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae7da2d2f4b2b02a3c997ff57779d97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338c6c83ab4abc895ac36ab888a55be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf067900155dc4935109b7e26819f978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1dfc77423431d864e2725a5be11b26.png)
您最近一年使用:0次