1 . 如图,在四棱锥
中,平面
平面
,
,
,
,
,
为棱
上一点,且
,
为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/6/7749788f-bd5d-4f3a-890c-1b866ef30593.png?resizew=211)
(1)证明:平面
平面
;
(2)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9132a5490b529ffd1ca0e665448ff62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15f5c876ee80d62472db4dc9e329fd80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccfb8347b22077e850fe698eabbb2f18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeef1db30212433062b3297569a7aafd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/6/7749788f-bd5d-4f3a-890c-1b866ef30593.png?resizew=211)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dd3d448c8474f0d0f8d3fd7766d9f4d.png)
您最近一年使用:0次
2022-07-05更新
|
1285次组卷
|
8卷引用:河南省豫北名校联考2021-2022学年高二下学期5月阶段性测试(四)文科数学试卷
河南省豫北名校联考2021-2022学年高二下学期5月阶段性测试(四)文科数学试卷(已下线)2022年全国高考乙卷数学(文)试题变式题9-12题江苏省南京市中华中学2021-2022学年高一下学期期末数学试题(已下线)2022年全国高考乙卷数学(文)试题变式题17-20题湖南省彬州市安仁县第一中学2021-2022学年高一下学期期末统考数学模拟试题(一)(已下线)8.6.1 空间直线、平面的垂直(精讲)-2022-2023学年高一数学一隅三反系列(人教A版2019必修第二册)(已下线)专题四 期末高分必刷解答题(32道)-《考点·题型·密卷》广东省肇庆市封开县广信中学2022-2023学年高一下学期第二次月考数学试题
名校
解题方法
2 . 如图,在四棱锥
中,底面ABCD为平行四边形,
,
,
,平面
平面ABCD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/4/7261bff4-2279-4b2e-8e3c-f4ea73280c20.png?resizew=297)
(1)证明:
;
(2)若
,E为AD的中点,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ea52361458ce2e49ed0fe99d8e6c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d6baf49925a5bcb359b542d45067c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/4/7261bff4-2279-4b2e-8e3c-f4ea73280c20.png?resizew=297)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8254b52b379a420c17d38334940b073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e73fe210736ce7b30b039d34587e3c1.png)
您最近一年使用:0次
2022-07-03更新
|
400次组卷
|
4卷引用:河南省新乡市封丘县第一中学2021-2022学年高二下学期期末数学文试题
解题方法
3 . 如图,在三棱锥
中,
,
,O为棱AC的中点.
![](https://img.xkw.com/dksih/QBM/2022/7/1/3013237568692224/3014442459144192/STEM/0df85cc4f66942289b322502b0037232.png?resizew=226)
(1)证明:
平面
;
(2)若点M在被AB上,且A到平面POM的距离为
,求平面POM将三棱锥
分成的左、右两部分的体积之比.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b370b7ca2390e41f13ccf2217fc85071.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4db3cc075b88dea374e92f94a178aa20.png)
![](https://img.xkw.com/dksih/QBM/2022/7/1/3013237568692224/3014442459144192/STEM/0df85cc4f66942289b322502b0037232.png?resizew=226)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若点M在被AB上,且A到平面POM的距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
您最近一年使用:0次
解题方法
4 . 如图,在正三棱柱
中,P为
的中点,Q为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/4/4366ec9f-16ba-42af-b87c-98be03c9caf0.png?resizew=203)
(1)求证:
平面ABC;
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/4/4366ec9f-16ba-42af-b87c-98be03c9caf0.png?resizew=203)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72221ee5b504d596ff799c0b356aa0ea.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e095775876648816d3af187806c5f027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/931f6f4f468271858b6a5f7b63453a8d.png)
您最近一年使用:0次
2022-07-02更新
|
324次组卷
|
2卷引用:河南省开封市2021-2022学年高二下学期期末数学文科试题
名校
解题方法
5 . 如图,在三棱柱
中,
平面
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/17/19ae1176-0f7a-486e-9022-b25ecf62816f.png?resizew=204)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
平面
.
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33255ce76e127e74548a41be4303321f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/17/19ae1176-0f7a-486e-9022-b25ecf62816f.png?resizew=204)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c97593e11d12376ccb6aa39006b03bcc.png)
您最近一年使用:0次
2022-05-26更新
|
901次组卷
|
2卷引用:河南省许平汝漯2021-2022学年高二下学期6月大联考数学(文科)试题
名校
解题方法
6 . 如图,已知四棱锥
的底面ABCD是矩形,
底面ABCD,
,M为BC的中点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/58af3e50-7c30-45d3-83fc-c070349a1c49.png?resizew=182)
(1)求四棱锥
的体积;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffddeafce03aae663bc823e2d5127c61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/186e5e7efe51fd25b9e38dc0fa23de9d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/1/58af3e50-7c30-45d3-83fc-c070349a1c49.png?resizew=182)
(1)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c650d59680db13009509578129f17f4.png)
您最近一年使用:0次
2022-05-10更新
|
562次组卷
|
2卷引用:河南名校联盟2021-2022学年高二下学期期中考试理科数学试题
7 . 如图,四棱锥
中,
,四边形PACQ为直角梯形,
,
,且
,
.
![](https://img.xkw.com/dksih/QBM/2022/4/28/2968165639356416/2973714898862080/STEM/edcd008b-3da3-473f-a1b9-cb53b927a950.png?resizew=167)
(1)求证:直线
平面PAB;
(2)若直线CA与平面PAB所成线面角为
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c74f1828d17c2059a2966fe960757541.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af620f6d204d310d8e3f267fdd6c3f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d9ef979b9f27a28cbda6923e888ccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28b0a8ce98e195c4fa22af9b71defc28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04af1c1856ba1c7cc969de81d77aabd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26a42b05e06fe34d66538930787bb3e.png)
![](https://img.xkw.com/dksih/QBM/2022/4/28/2968165639356416/2973714898862080/STEM/edcd008b-3da3-473f-a1b9-cb53b927a950.png?resizew=167)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
(2)若直线CA与平面PAB所成线面角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c4a3349d81e399a0d565613429cb795.png)
您最近一年使用:0次
2022-05-06更新
|
994次组卷
|
2卷引用:河南省漯河市高级中学2021-2022学年高二下学期期中考试数学(文)试题
名校
解题方法
8 . 如图,在四棱锥
中,底面ABCD是直角梯形,
,
,
,
,
,平面
平面ABCD,且
,E为BC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/27/43c6a96b-3efe-43db-8021-ce0c47d21dd0.png?resizew=186)
(1)证明:平面
平面PBD.
(2)若四棱锥
的体积为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d783fe7f3ce673d5d21281174e7a7968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32e1b499d6b25ee132abcdd3f3cd288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c383691e8d740830a865b12d66f7633.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/27/43c6a96b-3efe-43db-8021-ce0c47d21dd0.png?resizew=186)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d96357a07048ba79b8c84097d359d9.png)
(2)若四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c20567d122853e7c3119a1749ca8ccc4.png)
您最近一年使用:0次
2022-04-26更新
|
751次组卷
|
4卷引用:河南省许平汝漯联盟2021-2022学年高二下学期期中考试理科数学试题
名校
解题方法
9 . 如图,在四棱锥
中,
平面ABCD,底面ABCD是矩形,
,
,作
,交AD于点E,点F,G分别为线段PD,DC的中点.
![](https://img.xkw.com/dksih/QBM/2022/4/16/2959583193473024/2961379327459328/STEM/c1abd7db95c04ad9aa51e5686433adf4.png?resizew=234)
(1)证明:
平面BEF;
(2)求点E到平面BFG的距离.
![](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/f235e99b0b55ac252c4b18cc315dc114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d320f180419175d75eebc618cc458b39.png)
![](https://img.xkw.com/dksih/QBM/2022/4/16/2959583193473024/2961379327459328/STEM/c1abd7db95c04ad9aa51e5686433adf4.png?resizew=234)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
(2)求点E到平面BFG的距离.
您最近一年使用:0次
2022-04-19更新
|
381次组卷
|
2卷引用:九师联盟(河南省)2021-2022学年高二下学期4月联考文科数学试题
10 . 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)
您最近一年使用:0次