1 . 鸡公山,位于河南省信阳市境内,是中国四大避暑胜地之一,也是新中国第一批对外开放的全国八大景区之一,鸡公山是大别山的支脉,主峰鸡公头又名报晓峰,像一只引颈高啼的雄鸡,因名之鸡公山.主峰海拔814m,山势奇伟,泉清林翠,云海霞光,风景秀丽.旅游区管委会在山上建设别致凉亭供游客歇脚,如图为设计图,该凉亭的支撑柱高为
m,顶部为底面边长为2的正六棱锥,且侧面与底面所成的角都是45°.
![](https://img.xkw.com/dksih/QBM/2022/4/16/2959583138357248/2961376410140672/STEM/43258562-8104-4561-b12d-3769026a0f48.png?resizew=160)
(1)求该凉亭及其内部所占空间的大小;.
(2)在直线PC上是否存在点M,使得直线MA与平面
所成角的正弦值为
?若存在,请确定点M的位置;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adbd3e8cf8325999cde03adf845d3dd0.png)
![](https://img.xkw.com/dksih/QBM/2022/4/16/2959583138357248/2961376410140672/STEM/43258562-8104-4561-b12d-3769026a0f48.png?resizew=160)
(1)求该凉亭及其内部所占空间的大小;.
(2)在直线PC上是否存在点M,使得直线MA与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/814b61e61042874774c05cac41208024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
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名校
解题方法
2 . 如图所示,已知四边形
是边长为2的菱形,
,
,且
平面
,
//
,且异面直线
和
所成角的余弦值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fa63d3e323e0af20561b36a81aab19e.png)
![](https://img.xkw.com/dksih/QBM/2022/2/7/2911129309782016/2945848951496704/STEM/1a873fa6-070d-41be-bf30-10059d7118c7.png?resizew=185)
(1)求三棱锥
的体积
(2)求平面
与平面
所成角的余弦值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6569ff154c579d0f3bc2157bbdf53444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0042fbd04367d0df0fba2f59de72aa26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fab4d2a8ab12be628eb2ce03f0ae7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f79d7939c88e9702962e5917cad290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8120f2eeb724c756b5f84a14c6df527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0213c5787a5a6b38d11bceca5567f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fa63d3e323e0af20561b36a81aab19e.png)
![](https://img.xkw.com/dksih/QBM/2022/2/7/2911129309782016/2945848951496704/STEM/1a873fa6-070d-41be-bf30-10059d7118c7.png?resizew=185)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8040a570a0197daf7d1a7b50c89d9e2.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a06b68dc88cc22301870ad2819a1a2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1910c648c8bfa02218b2802f5bfbacfa.png)
您最近一年使用:0次
2022-03-28更新
|
252次组卷
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2卷引用:河南省郑州市第九中学2022-2023学年高二上学期第一次月考数学试题
名校
解题方法
3 . 已知正方体ABCD-
的棱长为2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/ccc35031-9655-47ad-a529-7e7377ce26b9.png?resizew=172)
(1)求三棱锥
的体积;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/ccc35031-9655-47ad-a529-7e7377ce26b9.png?resizew=172)
(1)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7254524620ba2247c642045efcb0a0a9.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa142bb96af98b846997e681609739f.png)
您最近一年使用:0次
2022-03-13更新
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3608次组卷
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7卷引用:河南宋基信阳实验中学2021-2022学年高二下学期转段考试(升高三)文科数学试题
河南宋基信阳实验中学2021-2022学年高二下学期转段考试(升高三)文科数学试题河南省新乡市第十一中学2021-2022学年高二下学期第二次月考文科数学试题2022年安徽省学业水平考前适应性考试数学试题陕西省咸阳市2021-2022学年高一上学期期末数学试题(已下线)高一数学下学期期末精选50题(基础版)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)(已下线)第04讲 空间直线、平面的垂直 (高频考点—精讲)-1专题07B立体几何解答题
4 . 如图,AB是⊙O的直径,点P是⊙O圆周上异于A、B的一点,
平面PAB,
,
.
![](https://img.xkw.com/dksih/QBM/2022/3/8/2931920521314304/2933904042500096/STEM/3add5fae-d5be-4597-8f84-d3d291e7a96c.png?resizew=144)
(1)求证:平面
平面PAD;
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c58bafdd3bb54ba3491b49ab60b172f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e70dccdfccce3bb76a145b6d9d5be9.png)
![](https://img.xkw.com/dksih/QBM/2022/3/8/2931920521314304/2933904042500096/STEM/3add5fae-d5be-4597-8f84-d3d291e7a96c.png?resizew=144)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4e66a2c8440276c9608a8abe834083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c10c16d2d9d22c4b34ddd965e26aa0d7.png)
您最近一年使用:0次
2022-03-11更新
|
608次组卷
|
4卷引用:河南省信阳市2021-2022学年高二下学期期中教学质量检测数学(文科)试题
名校
解题方法
5 . 如图所示,在四棱锥
中,底面
为直角梯形,平面
平面
,
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2022/3/7/2931316583587840/2932502327058432/STEM/5b6d3ec2-76e6-4d7c-af7e-b090164fea99.png?resizew=180)
(1)求证:
,并且求三棱锥
的体积;
(2)求直线
与平面
所成角的正弦值.
![](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/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b0e30c61f4433ca0d6b7c30d82632a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678069acbf21579b42a786385b154c8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e628d8d153b597967cbcb6e02250b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/2022/3/7/2931316583587840/2932502327058432/STEM/5b6d3ec2-76e6-4d7c-af7e-b090164fea99.png?resizew=180)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d84733f9dc908ceb11459cc2aed580ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddfe0ccf24d760c77535a70c92dad145.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
2022-03-09更新
|
296次组卷
|
2卷引用:河南省周口市周口恒大中学2023-2024学年高二上学期9月月考数学试题
名校
解题方法
6 . 如图,四棱锥
中,底面ABCD为直角梯形,
,
平面ABCD,
,
,M为PC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/430c7b11-1d02-43b6-859c-caa8b33188be.png?resizew=201)
(1)求证:平面
平面PCD;
(2)若
,求四棱锥
的体积.
(3)在(2)的条件下,求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/666c7e13a7999bd5970c1e478a665935.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8901560f35f7278c84e5bbc000f5f47b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/430c7b11-1d02-43b6-859c-caa8b33188be.png?resizew=201)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c1a03f93b56a1fb0b57d20d53b4323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
(3)在(2)的条件下,求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1636b4530c0b42d0e0b649e90e3b9e85.png)
您最近一年使用:0次
2022-01-11更新
|
450次组卷
|
3卷引用:河南省许昌市禹州市高级中学菁华校区2022-2023学年高二上学期期末数学试题
河南省许昌市禹州市高级中学菁华校区2022-2023学年高二上学期期末数学试题广东省深圳市龙岗区德琳学校高中部2020-2021学年高一下学期期中数学试题(已下线)高一数学下学期期中全真模拟卷(1)-2021-2022学年高一数学考试满分全攻略(人教A版2019必修第二册)(原卷版)
名校
解题方法
7 . 已知正三棱柱
的底面边长为2,D是
的中点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2586e0bb827b0f1739e6ab36c0d62c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/5d932a24-62fa-4208-af51-d9a1cebe80aa.png?resizew=261)
(1)求三棱柱
的体积
(2)求直线
与平面
所成角的正弦值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2586e0bb827b0f1739e6ab36c0d62c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/5d932a24-62fa-4208-af51-d9a1cebe80aa.png?resizew=261)
(1)求三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a52848aff08399a36f217356007a4b.png)
您最近一年使用:0次
2021-11-23更新
|
620次组卷
|
4卷引用:河南省巩义市重点校2022-2023学年高二上学期第四次考试数学试题
名校
解题方法
8 . 如图所示,△BCD与△MCD都是边长为2的等边三角形,平面MCD
平面BCD,AB
平面BCD,AB=2
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/9d052dc2-c261-4bfc-8a38-c2575763a284.png?resizew=178)
(1)求点A到平面MBC的距离;
(2)求三棱锥M-ACB的体积;
(3)求二面角A-MD-B的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/15/9d052dc2-c261-4bfc-8a38-c2575763a284.png?resizew=178)
(1)求点A到平面MBC的距离;
(2)求三棱锥M-ACB的体积;
(3)求二面角A-MD-B的正弦值.
您最近一年使用:0次
9 . 如图所示,在四棱柱
中,底面
是菱形,
.
![](https://img.xkw.com/dksih/QBM/2021/11/5/2844837721964544/2845017587367936/STEM/539f5d39-a074-4603-9db1-a3c087837d14.png?resizew=235)
(1)证明:平面
平面
;
(2)若四边形
是正方形,
,求四棱柱
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e735911ba4cd7f8fca6b3f65d705b573.png)
![](https://img.xkw.com/dksih/QBM/2021/11/5/2844837721964544/2845017587367936/STEM/539f5d39-a074-4603-9db1-a3c087837d14.png?resizew=235)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(2)若四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a05e0ab55e325fb3b85fc8ca9c27c76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
您最近一年使用:0次
2021-11-05更新
|
191次组卷
|
3卷引用:河南省焦作市普通高中2021-2022学年高二上学期期中考试文科数学试题
河南省焦作市普通高中2021-2022学年高二上学期期中考试文科数学试题河南省焦作市普通高中2021-2022学年高二上学期期中数学理科试题(已下线)上海市静安区2023届高三二模数学试题变式题16-21
10 . 如图,在四棱锥
中,
,
,
,
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/177a107d-85c3-4ecc-a9c0-ffa70ca22c2e.png?resizew=162)
(1)在线段
上是否存在一点
使得
平面
?若存在,求出
的位置;若不存在,请说明理由;
(2)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99da52604d90b4772725a2632a39dbb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ae8a050d7159d4296c2409e5bc0bf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a8256dc97e0101783f83159d35eeadf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9143934f4635574d5611ffd05a650ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/177a107d-85c3-4ecc-a9c0-ffa70ca22c2e.png?resizew=162)
(1)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99da52604d90b4772725a2632a39dbb6.png)
您最近一年使用:0次
2021-10-24更新
|
480次组卷
|
3卷引用:河南省中原名校2021-2022学年高二上学期期末联考文科数学试题