1 . 如图所示,圆锥的侧面积是底面积的2倍,线段
为圆锥底面
的直径,在底面内以线段
为直径作
,点
为
上异于点
的动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/c4d207af-88a2-49bb-ba8d-c509c87d5dfa.png?resizew=175)
(1)证明:平面
平面
;
(2)已知
,当三棱锥
的体积最大时,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fef27cb7cb1b666c1734c65a7aa9aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fef27cb7cb1b666c1734c65a7aa9aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f4411b37e8ed03b1841906af3bf912f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/c4d207af-88a2-49bb-ba8d-c509c87d5dfa.png?resizew=175)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c471d86d6c1c31f0466c5934ca58070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2b5f083dd0e4ff840eb8be0ea0087f6.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/308ad15630a0d58be043375239f4073f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a5b827a4df552ef718b5b772fa2b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b74a32c8ccd8a3632c8d79e5eb51cc.png)
您最近一年使用:0次
2020-08-19更新
|
140次组卷
|
4卷引用:辽宁省实验中学2020届高三下学期学期第下学期五次模拟考试数学文科试卷
辽宁省实验中学2020届高三下学期学期第下学期五次模拟考试数学文科试卷辽宁省锦州市黑山县黑山中学2020届高三下学期考前模拟训练数学(文)试题普通高等学校招生国统一考试2020-2021学年高三上学期 数学(文)考向卷(八)(已下线)专题20 立体几何综合-2020年高考数学(文)母题题源解密(全国Ⅱ专版)
解题方法
2 . 如图,在三楼柱ABC﹣A1B1C1中,平面ACC1A1⊥平面ABC,四边形ACC1A1是正方形,点D是棱BC的中点,点E是线段BB1上一点,AB=4,AA1=2,BC=2
.
![](https://img.xkw.com/dksih/QBM/2020/7/24/2512917842698240/2513024859660288/STEM/80a49063f8184a56b8e3d4a4f939c172.png?resizew=319)
(1)求证:AB⊥CC1;
(2)求三棱锥E﹣ADC1体积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://img.xkw.com/dksih/QBM/2020/7/24/2512917842698240/2513024859660288/STEM/80a49063f8184a56b8e3d4a4f939c172.png?resizew=319)
(1)求证:AB⊥CC1;
(2)求三棱锥E﹣ADC1体积的最大值.
您最近一年使用:0次
名校
解题方法
3 . 如图,在边长为4的菱形ABCD中,∠DAB=60°,点E,F分别是边CD,CB的中点,AC∩EF=O,沿EF将△CEF翻折到△PEF,连接PA,PB,PD,得到如图的五棱锥P﹣ABFED,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/3f48f92e-887d-4a97-904d-e3e698ca141b.png?resizew=365)
(1)求证:
;
(2)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b22c064739c95b84333d52e033668a58.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/3f48f92e-887d-4a97-904d-e3e698ca141b.png?resizew=365)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/712f7375b4ede5f75c0d81870c0f86af.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a43c429d2676774d09e2509d9e26a0d.png)
您最近一年使用:0次
2020-07-24更新
|
198次组卷
|
3卷引用:辽宁省沈阳市第二中学2020届高三下学期第五次模拟考试数学(文)试题
辽宁省沈阳市第二中学2020届高三下学期第五次模拟考试数学(文)试题辽宁省沈阳二中2020届高三高考数学(文科)五模试题(已下线)考点35 空间几何体的表面积和体积(考点专练)-备战2021年新高考数学一轮复习考点微专题
4 . 如图,长方体ABCD﹣A1B1C1D1的底面ABCD是正方形,点E在棱AA1上,BE⊥EC1.
![](https://img.xkw.com/dksih/QBM/2020/7/24/2512874120536064/2512930852503553/STEM/95b1b5b73d994c8e9ea1dae6940e09c6.png?resizew=150)
(1)证明:平面CBE⊥平面EB1C1;
(2)若AE=A1E,AB=2,求三棱锥C﹣EBC1的体积.
![](https://img.xkw.com/dksih/QBM/2020/7/24/2512874120536064/2512930852503553/STEM/95b1b5b73d994c8e9ea1dae6940e09c6.png?resizew=150)
(1)证明:平面CBE⊥平面EB1C1;
(2)若AE=A1E,AB=2,求三棱锥C﹣EBC1的体积.
您最近一年使用:0次
解题方法
5 . 如图,在三棱锥A﹣BCD中,O为AB的中点,点F在线段AD上,DC=AC=BC=
,AB=2,DO⊥平面ABC.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/99e530d9-1a0a-4424-b0eb-955d8713c8b2.png?resizew=163)
(1)若OF∥平面BCD,求证:点F为线段AD的中点;
(2)求点A到平面BCD的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/99e530d9-1a0a-4424-b0eb-955d8713c8b2.png?resizew=163)
(1)若OF∥平面BCD,求证:点F为线段AD的中点;
(2)求点A到平面BCD的距离.
您最近一年使用:0次
名校
解题方法
6 . 如图,等腰梯形ABCD中,AB∥CD,AD=AB=BC=1,CD=2,E为CD的中点,将△ADE沿AE折到△APE的位置.
(1)证明:AE⊥PB;
(2)当四棱锥PABCE的体积最大时,求点C到平面PAB的距离.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/31/b2bae448-0250-496b-a682-de476c0e2311.png?resizew=373)
(1)证明:AE⊥PB;
(2)当四棱锥PABCE的体积最大时,求点C到平面PAB的距离.
您最近一年使用:0次
2020-11-10更新
|
118次组卷
|
7卷引用:【省级联考】东北三省四市2019届高三第一次模拟数学(文)试题
【省级联考】东北三省四市2019届高三第一次模拟数学(文)试题【市级联考】东北三省四市2019届高三第一次模拟数学(文)试题【市级联考】吉林省长春市普通高中2019届高三质量检测(三)数学(文科)试题黑龙江省大庆铁人中学2020届高三考前模拟训练文科数学试题(已下线)专题8.5 立体几何中的综合问题-2021年高考数学(文)一轮复习-题型全归纳与高效训练突破(已下线)专题8.6 翻折与探索性问题(精练)-2021年高考数学(文)一轮复习讲练测四川省乐山市峨眉第二中学校2022-2023学年高二下学期期中数学文科试题
名校
解题方法
7 . 如图1,在直角梯形
中,
,
,
,
,
,点E在
上,且
,将三角形
沿线段
折起到
的位置,
(如图2).
![](https://img.xkw.com/dksih/QBM/2020/7/9/2502381914177536/2503478292307968/STEM/c232da63572242c7bb52ca0005830370.png?resizew=400)
(Ⅰ)求证:平面
平面
;
(Ⅱ)在线段
上存在点F,满足
,求平面
与平面
所成的锐二面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd8e727e4efc22b49649f71ae9c9d84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cedd51383f8f047f565191b128cec637.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c3ec174b1ce835cc8737ff6ce57e52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d76905ac2451077244e5cea42e173c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/689b95a2eeb841dd3a0a3a6dfa3be8fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6c2dad46a9052a4185a4f7b4ae8a2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e99998f33ad6edab18180627d4903dcc.png)
![](https://img.xkw.com/dksih/QBM/2020/7/9/2502381914177536/2503478292307968/STEM/c232da63572242c7bb52ca0005830370.png?resizew=400)
(Ⅰ)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d96357a07048ba79b8c84097d359d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ff27eea7545bb06f9472f91290c54e.png)
(Ⅱ)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80382a14419cdf637be277f544dd8e27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6c2dad46a9052a4185a4f7b4ae8a2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20af148464904e21f4374cc8fb886fba.png)
您最近一年使用:0次
2020-07-11更新
|
351次组卷
|
3卷引用:东北三省三校(哈师大附中、东北师大附中、辽宁省实验中学)2020届高三高考数学(理科)三模试题
8 . 多面体
中,
为等边三角形,
为等腰直角三角形,
平面
,
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/6be6fa20-d8cf-48bc-9d86-29a68822ad89.png?resizew=137)
(1)求证:
;
(2)若
,
,求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986ba572d8373df48c996f8c8611498c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cb97395ebc5ee1b212afb7a97b985c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c372d059202ec388960b125d4a87dc84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61510c34c5795d7261569b4d09098271.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810ee7bc82b6f452afb3fc18691abc3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a28d6477c85c5a4ac410a884e92fbe53.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/6be6fa20-d8cf-48bc-9d86-29a68822ad89.png?resizew=137)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38b5c1c5518b9332a2fb209c3621c700.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc1a0e79e49e224c198af0c37405a3ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beba9c5993784964af81ec070b168456.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/986ba572d8373df48c996f8c8611498c.png)
您最近一年使用:0次
2020-07-08更新
|
1109次组卷
|
3卷引用:辽宁省辽阳市2020届高三下学期第三次模拟考试数学(文)试题
9 . 如图,长方体
的底面
是正方形,点
在棱
上,
.
![](https://img.xkw.com/dksih/QBM/2020/7/7/2500825870639104/2500908985344000/STEM/f7c037f5728c4b1bbad1872254f4fbe0.png?resizew=154)
(1)证明:平面
平面
;
(2)若
,
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/801a443c35d6c50b859c54e039905bb0.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/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c810d9d154dbbc0cef6ab8ffcd488045.png)
![](https://img.xkw.com/dksih/QBM/2020/7/7/2500825870639104/2500908985344000/STEM/f7c037f5728c4b1bbad1872254f4fbe0.png?resizew=154)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a06781fd124cad40fa5fd120b074157f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c4f474f2c144be8703517ef72b98a7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7956d36499b97a127c725e10bc58fca3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae3bb435402983b10f311dc84989de4.png)
您最近一年使用:0次
2020-07-07更新
|
273次组卷
|
2卷引用:辽宁省沈阳市2020届高三年级教学质量监测(三)数学(文科)试题
解题方法
10 . 在三棱锥
中,
平面
,
为
的中点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/32ded868-f4eb-4c5b-a775-610efa1c61b2.png?resizew=146)
(1)证明:
平面
.
(2)若
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92a3680ec97ccbb82b6e1ff78ac10b7c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/11/32ded868-f4eb-4c5b-a775-610efa1c61b2.png?resizew=146)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e4e887f25b10f9f1833fe4fb355b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64eb31601464364be2baf4aa87404bcd.png)
您最近一年使用:0次
2020-06-29更新
|
696次组卷
|
5卷引用:辽宁省盘锦市辽河油田第三高级中学2020届高三下学期三模数学(文)试题