名校
解题方法
1 . 如图,在棱长为2的正方体
中,
是棱
的中点,
是
与
的交点.
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e22ebcc4aa98d46366df48f751a5f368.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2978e60a50f25e124aa7e325102b3617.png)
您最近一年使用:0次
7日内更新
|
1176次组卷
|
4卷引用:陕西省榆林市2022-2023学年高二下学期质量检测文科数学试卷
陕西省榆林市2022-2023学年高二下学期质量检测文科数学试卷(已下线)核心考点6 立体几何中组合体 A基础卷 (高一期末考试必考的10大核心考点) 陕西省西安市第一中学2024届高三第十六次模拟考试数学(文科)试题(已下线)专题08 立体几何异面直线所成角、线面角、面面角及平行和垂直的证明 -《期末真题分类汇编》(北师大版(2019))
名校
解题方法
2 . 如图所示,在四棱锥
中,
平面
,
,
,
是
的中点,
,
.
![](https://img.xkw.com/dksih/QBM/2023/11/24/3375040314818560/3375070155898880/STEM/84943f3c3953461fb55cb7d164f49154.png?resizew=257)
(1)证明:
平面
;
(2)若二面角
的平面角的大小为
,求四棱锥
的体积.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04a93f5289c1483bc39b0125fdc8dd67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea02307e6da633304ede631c3c374261.png)
![](https://img.xkw.com/dksih/QBM/2023/11/24/3375040314818560/3375070155898880/STEM/84943f3c3953461fb55cb7d164f49154.png?resizew=257)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a6d5aaf764583992b9ec1e7dea8f5f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
2023-11-24更新
|
614次组卷
|
2卷引用:四川省绵阳市南山中学实验学校2023-2024学年高二上学期期末模拟数学试题(六)
3 . 如图,已知圆锥的顶点为
,底面圆心为
,高为
,底面半径为2.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/19/0eb400c9-84f0-495a-a911-878c13ad0693.png?resizew=152)
(1)求该圆锥的侧面积;
(2)设
为该圆锥的底面半径,且
,
为
的中点,求二面角
的大小(用反三角表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/19/0eb400c9-84f0-495a-a911-878c13ad0693.png?resizew=152)
(1)求该圆锥的侧面积;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f47ddc7c9fb41942160e3cafcf756776.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ccc37b189fa2cbc269ca0b233dac37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/142b0739dc0ee9499a7df34a4e9dc726.png)
您最近一年使用:0次
2023-11-21更新
|
188次组卷
|
2卷引用:内蒙古通辽市科左中旗民族职专·实验高中2023-2024学年高二上学期期末数学试题
名校
解题方法
4 . 正四棱锥
中,
,
,其中
为底面中心,
为
上靠近
的三等分点.
平面
;
(2)求四面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764829cc2c763b6aca0665aa143e304e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3df5935c893580c77ab6fa6eb0a70bdb.png)
(2)求四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0242f1d6a2dd3c0d14961339164e298.png)
您最近一年使用:0次
2023-11-13更新
|
1231次组卷
|
10卷引用:西藏自治区拉萨市部分学校2023-2024学年高二上学期期末联考数学(理)试题
西藏自治区拉萨市部分学校2023-2024学年高二上学期期末联考数学(理)试题上海市文来中学2024届高三上学期期中数学试题(已下线)考点9 垂直的判定与性质 2024届高考数学考点总动员四川省南充市阆中中学校2024届高三一模数学(文)试题(已下线)模块三 专题4 大题分类练(立体几何)基础夯实练新疆维吾尔自治区喀什地区喀什十四校2023-2024学年高二上学期期末数学试题青海省西宁市2024届高三上学期期末联考数学(文)试题(已下线)第12讲 8.6.2直线与平面垂直的判定定理(第1课时)-【帮课堂】(人教A版2019必修第二册)青海省西宁市海湖中学2023-2024学年高二下学期开学考试数学试卷(已下线)重难点专题10 轻松解决空间几何体的体积问题-【帮课堂】(苏教版2019必修第二册)
5 . 如图,在正三棱柱
中,
,此三棱柱的体积为
,P为侧棱
上点,且
,H、G分别为AB、
的中点.
![](https://img.xkw.com/dksih/QBM/2023/11/3/3360088469741568/3361922927149056/STEM/df5a3e5641af4bd6be23709cfe777f4e.png?resizew=180)
(1)求此三棱柱的表面积;
(2)求异面直线
与
所成角的大小;
(3)求
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b27567d43c5b91382ee3d7ca708ee422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98823cbc09ca52df1fbcc446eba3e44f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/2023/11/3/3360088469741568/3361922927149056/STEM/df5a3e5641af4bd6be23709cfe777f4e.png?resizew=180)
(1)求此三棱柱的表面积;
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ad3a1ea6790177130e16c2124984087.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ad3a1ea6790177130e16c2124984087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
您最近一年使用:0次
6 . 我国古代数学名著《九章算术》,将底面为矩形且有一条侧棱垂直于底面的四棱锥称为“阳马”.如图所示,在长方体
中,已知
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/31/064926f8-580d-47cb-ba38-0fa73946e3aa.png?resizew=134)
(1)求证:四棱锥
是一个“阳马”,并求该“阳马”的体积;
(2)求该“阳马”
的外接球的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/31/064926f8-580d-47cb-ba38-0fa73946e3aa.png?resizew=134)
(1)求证:四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec35c2182c5e0c80b766adceb058e5f.png)
(2)求该“阳马”
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec35c2182c5e0c80b766adceb058e5f.png)
您最近一年使用:0次
解题方法
7 . 如图所示,从底面半径为
,高为
的圆柱中,挖去一个底面半径为
且与圆柱等高的圆柱,求原圆柱的表面积
与挖去圆柱后的几何体的表面积
的比值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/878e89b6eca35e34c863e832a2c661db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a24d95e0548b340af8783a57bdfd05b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/17/6f77c7df-2936-4345-b3cd-af25e8ac3e17.png?resizew=135)
您最近一年使用:0次
2023-10-27更新
|
325次组卷
|
4卷引用:内蒙古自治区鄂尔多斯市鄂托克旗高级中学2022-2023学年高一下学期期末数学试题
内蒙古自治区鄂尔多斯市鄂托克旗高级中学2022-2023学年高一下学期期末数学试题8.3.2.1圆柱、圆锥、圆台的表面积和体积练习(已下线)专题8.11 立体几何初步全章十四大压轴题型归纳(拔尖篇)-举一反三系列(已下线)8.3.2 圆柱、圆锥、圆台、球的表面积和体积-同步精品课堂(人教A版2019必修第二册)
名校
解题方法
8 . 如图,在三棱柱
中,
平面ABC,
,
,
,点D,E分别在棱
和棱
上,且
,
,M为棱
的中点.
![](https://img.xkw.com/dksih/QBM/2023/9/24/3331550634868736/3332899792420864/STEM/b7d74dab205e42c4947507df95478a25.png?resizew=156)
(1)求证:
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8bfe2553e852df73185d017c0a62fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209acf15985d1ea1ad86fc4a37e38c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c122ca7141c43c15c783968f5f0dbc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0761165f1176f3a5fe4f7b052832316d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/2023/9/24/3331550634868736/3332899792420864/STEM/b7d74dab205e42c4947507df95478a25.png?resizew=156)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8973bcb7d87303a0b5fba04a801019b9.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abfb4848802216eac7b065099d6f35ac.png)
您最近一年使用:0次
2023-09-26更新
|
297次组卷
|
2卷引用:四川省南充高级中学2022-2023学年高二上学期期末考试文科数学试题
解题方法
9 . 在棱长为1的正方体
中,E,F,G分别是
的中点
(1)求AE的长;
(2)求EF与CG所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcbd33d99bce4cded5138b6a52fb6fd8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/22/118136e5-3839-4c8e-bcc3-4afeb7fa1b81.png?resizew=153)
(1)求AE的长;
(2)求EF与CG所成角的余弦值.
您最近一年使用:0次
2023-08-22更新
|
315次组卷
|
2卷引用:河南省许昌市2022-2023学年高二上学期期末文科数学试题
解题方法
10 . 如图,在直四棱柱
中,底面是边长为2的菱形,
,O分别为上、下底的中心,
,点
是
的中点.
平面
;
(2)若三棱锥
的体积为
,求棱柱的侧面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7dbf31dfd36aa456a63bafea8bc1985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6afb5c6e2d0469bfdec81be42542bdc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc852e3603a21a93affc70812b2f2622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)若三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7260881c6fb7470a33cc809c34df40ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
您最近一年使用:0次
2023-08-12更新
|
566次组卷
|
5卷引用:辽宁省鞍山市台安县高级中学2022-2023学年高一下学期期末数学试题
辽宁省鞍山市台安县高级中学2022-2023学年高一下学期期末数学试题山东省潍坊市高密市第三中学2023-2024学年高二上学期8月月考数学试题辽宁省抚顺德才高级中学2023-2024学年高二上学期期初考试数学(北大班)试题(已下线)专题08立体几何期末14种常考题型归类(1)-期末真题分类汇编(人教B版2019必修第四册)(已下线)专题08 立体几何异面直线所成角、线面角、面面角及平行和垂直的证明 -《期末真题分类汇编》(北师大版(2019))