1 . 如图所示,圆锥的底面半径为4,侧面积为
,线段AB为圆锥底面
的直径,
在线段AB上,且
,点
是以BC为直径的圆上一动点;
![](https://img.xkw.com/dksih/QBM/2022/5/26/2987747278184448/2989158358548480/STEM/dede9fe2b84c4173a4ca2b4548c1bc01.png?resizew=186)
(1)当
时,证明:平面
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15b63176f43bc7a0654d0f6f45e7429.png)
(2)当三棱锥
的体积最大时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0323e5b0f5982d68422190dbe158631c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d9cbc8be03e4b5e76338d65be175973.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/2022/5/26/2987747278184448/2989158358548480/STEM/dede9fe2b84c4173a4ca2b4548c1bc01.png?resizew=186)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6773669d3f75b70ba37e5106efc482ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15b63176f43bc7a0654d0f6f45e7429.png)
(2)当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a9ec3b527947cad9caa4537e0cb7e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2425afeae790f548529e24c81a40560c.png)
您最近一年使用:0次
名校
2 . 如图,在三棱柱
中,平面
平面
,四边形
是矩形,
是菱形,
分别是
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/19/9c635367-5edc-4881-a709-454dad64e54a.png?resizew=160)
(1)求证:
平面
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cdaadeae37736a1e6dd93fa1fe712f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80af97f1dc2fa60681380ef6faefab0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36690681ee4f3dc5008cc89dc5cc4b0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846071242f981289741ad19f4e7190cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efa3d9405c2bbfc6770e93477bf1f059.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/19/9c635367-5edc-4881-a709-454dad64e54a.png?resizew=160)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4560fa4ad459b58b723c74bd24e51ebf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9539f8fb13345b449274b67bbda995db.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02f0c5dbb76086c87079141afc94685d.png)
您最近一年使用:0次
2022-05-19更新
|
515次组卷
|
3卷引用:湖南省长沙市明德中学2022届高三下学期二模数学试题
名校
3 . 如图,在平行四边形ABCM中,AB=AC=3,∠ACM=90°,以AC为折痕将△ACM折起,使点M到达点D的位置,且AB⊥DA.
![](https://img.xkw.com/dksih/QBM/2022/5/9/2975686414393344/2976644283752448/STEM/f211d22e-9382-4b82-bb5d-386a6ebb4e17.png?resizew=269)
(1)证明:平面ACD⊥平面ABC;
(2)Q为线段AD上一点,P为线段BC上一点,且BP=DQ=
DA.
①求三棱锥Q−ABP的体积;
②求二面角Q−AP−C的余弦值.
![](https://img.xkw.com/dksih/QBM/2022/5/9/2975686414393344/2976644283752448/STEM/f211d22e-9382-4b82-bb5d-386a6ebb4e17.png?resizew=269)
(1)证明:平面ACD⊥平面ABC;
(2)Q为线段AD上一点,P为线段BC上一点,且BP=DQ=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
①求三棱锥Q−ABP的体积;
②求二面角Q−AP−C的余弦值.
您最近一年使用:0次
2022-05-10更新
|
2079次组卷
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6卷引用:湖南省长沙市明德中学2021-2022学年高一下学期期中数学试题
湖南省长沙市明德中学2021-2022学年高一下学期期中数学试题山东省淄博市博山区、沂源县联考2021-2022学年高一下学期6月份月考数学试题山东省临沂市平邑第一中学新校区2021-2022学年高一下学期6月月考数学试题(已下线)专题8.15 空间中线面的位置关系大题专项训练(30道)-2022-2023学年高一数学举一反三系列(人教A版2019必修第二册)专题12空间中直线、平面的平行与垂直关系(解答题)(已下线)8.6.3平面与平面垂直——课后作业(基础版)
名校
4 . 已知四棱锥
中,底面
是正方形,
是正三角形,
平面
,E、F、G、O分别是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/392f9809-1c9a-4e58-9983-8636ecfb9152.png?resizew=214)
(1)求证:
平面
;
(2)求平面
与平面
夹角的大小;
(3)问:线段
上是否存在点M,使得直线
与平面
所成角的大小为
,若存在,求出
的值;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/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c84392a59f8bc3ea4d8b873ca6a9bdc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/392f9809-1c9a-4e58-9983-8636ecfb9152.png?resizew=214)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)问:线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e9e953a4a5f98c96bbe67cbaadf76d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9a386b370ffb5739049b3391112b5d2.png)
您最近一年使用:0次
2022-04-19更新
|
937次组卷
|
2卷引用:湖南省长沙市长郡中学2021-2022学年高一下学期期末综合复习数学试题
名校
解题方法
5 . 如图所示,已知在四棱锥
中,底面ABCD是边长为2的菱形,
,侧棱
,
,过点A的平面与侧棱PB,PD,PC相交于点E,F,M,且满足:
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/9/f0c96c99-b051-4bbe-acd2-bb228824de82.png?resizew=226)
(1)求证:直线
平面PAD;
(2)求证:直线
平面AEMF;
(3)求平面MDB与平面AEMF所成二面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/983ec5b9fd5d080e6e505d36edbfd300.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d0710321d97361e5782124bbf7f0c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b30155e0e3cf7c5146d3311e5b8da93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dca0fddd44a2a325754baf9452fe90a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/9/f0c96c99-b051-4bbe-acd2-bb228824de82.png?resizew=226)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963a91995abd4927d75406d16e10a81f.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
(3)求平面MDB与平面AEMF所成二面角的正弦值.
您最近一年使用:0次
2022-07-07更新
|
1273次组卷
|
3卷引用:湖南省长沙市四校联考2021-2022学年高一下学期期末数学试题
名校
6 . 如图,
是半球的直径,
为球心,
依次是半圆
上的两个三等分点,
是半球面上一点,且
,
![](https://img.xkw.com/dksih/QBM/2022/6/2/2992657885069312/2994303654756352/STEM/a8454b57-25b9-4515-8ac4-e5e4472e5be3.png?resizew=249)
(1)证明:平面
平面
;
(2)若点
在底面圆内的射影恰在
上,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c6eff038537d5fdae6e9741e2bd9dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c16bb6dfa23ed5b89e42c95ce0590eae.png)
![](https://img.xkw.com/dksih/QBM/2022/6/2/2992657885069312/2994303654756352/STEM/a8454b57-25b9-4515-8ac4-e5e4472e5be3.png?resizew=249)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d24305d21268a9b67cf6a8daae6bbe4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6b79de40c8517ab2650999401d7c3c.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f42a997b72568fa71bd29bedd8be6f1.png)
您最近一年使用:0次
2022-06-04更新
|
3376次组卷
|
6卷引用:湖南师范大学附属中学2020-2021学年高一下学期期末数学试题
湖南师范大学附属中学2020-2021学年高一下学期期末数学试题(已下线)第02讲 玩转立体几何中的角度、体积、距离问题-【暑假自学课】2022年新高二数学暑假精品课(苏教版2019选择性必修第一册)湖北省武汉市新高考联合体2021-2022学年高一下学期期末数学试题安徽省合肥六校联盟2022-2023学年高一下学期期末联考数学试卷(已下线)第8章立体几何初步(基础、典型、易错、压轴)分类专项训练专题12空间中直线、平面的平行与垂直关系(解答题)
名校
解题方法
7 . 如图,在四棱锥
中,底面ABCD是菱形,
,
,
,
底面ABCD,
,点E在棱PD上,且
.
平面ACE;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05740f0c6071846227dc0ec177ad15e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a23f01af749100e1888bba06268843db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae890f9e8b32aa53a54158f24f4a87bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc72a44dad13532cb9ddcc64bd78105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5102c216393e133fa25dba98cd78535.png)
您最近一年使用:0次
2023-05-10更新
|
1700次组卷
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11卷引用:湖南省长沙市第一中学2019-2020学年高一上学期期末数学试题
湖南省长沙市第一中学2019-2020学年高一上学期期末数学试题湖南省长沙市长郡中学2022-2023学年高一下学期期中数学试题湖南省长沙市明德中学2022-2023学年高一下学期期中数学试题【全国百强校】重庆市江津中学、合川中学等七校2018-2019学年高二上学期期末考试数学(理科)试题2020届江西省分宜中学高三上学期第一次段考数学(理)试题江苏省南京师范大学附属中学江宁分校2020-2021学年高一下学期第二次月考数学试题第13章:立体几何初步-基本图形及位置关系(A卷基础卷)-2020-2021学年高一数学必修第二册同步单元AB卷(新教材苏教版)广东省梅州市三校2020-2021学年高二下学期4月联考数学试题广西壮族自治区河池八校同盟体2022-2023学年高一下学期5月月考数学试题福建师范大学附属中学2022-2023学年高一下学期期末考试数学试题湖南省岳阳市岳阳县第一中学2023-2024学年高一下学期4月期中考试数学试题
名校
解题方法
8 . 如图,在三棱锥
中,平面
平面BCD,
,O为BD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/03a165cc-5aa4-4648-b144-0aecffebc1f4.png?resizew=190)
(1)证明:
;
(2)若
是边长为2的等边三角形,点E在棱AD上,
且二面角
的大小为
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f48dc419adb17eb12220f07480b077b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/03a165cc-5aa4-4648-b144-0aecffebc1f4.png?resizew=190)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21be01a95cdd3149512bf95d6084fdd6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4807ca16360c0cca436e59d4be98f626.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46d76c5ac5c9f0a2ec064487c02c476e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36701a8b4c9771070912b1c23a5c1950.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f48dc419adb17eb12220f07480b077b8.png)
您最近一年使用:0次
名校
解题方法
9 . 在四棱锥P−ABCD中,AD∥BC,AB=BC=CD=PC=PD=2,PA=AD=4.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/b67d9b3e-560f-4f2a-9a2f-a28ff3a68792.png?resizew=180)
(1)求证:平面PCD⊥平面ABCD;
(2)求二面角B−PC−D的正弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/b67d9b3e-560f-4f2a-9a2f-a28ff3a68792.png?resizew=180)
(1)求证:平面PCD⊥平面ABCD;
(2)求二面角B−PC−D的正弦值.
您最近一年使用:0次
2022-02-28更新
|
696次组卷
|
2卷引用:湖南省长沙市第一中学2021-2022学年高三上学期月考(五)数学试题
名校
10 . 如下图所示,四棱锥
中,底面
为矩形,
底面
,
,
,点
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/2021/12/17/2874427231551488/2875153242931200/STEM/3d451a03-92f0-4d4b-a835-bd749af95dec.png?resizew=237)
(1)证明:平面
平面
;
(2)求二面角
的平面角的余弦值.
![](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/f235e99b0b55ac252c4b18cc315dc114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/2021/12/17/2874427231551488/2875153242931200/STEM/3d451a03-92f0-4d4b-a835-bd749af95dec.png?resizew=237)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28f06184f021ac21d72de1c7f55b0778.png)
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