1 . 如图,四棱锥的底面
是边长为
的菱形,
,
,
,平面
平面
,E,F分别为
,
的中点.
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6c2dad46a9052a4185a4f7b4ae8a2e.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d246f9eceab371ebf47a47c2f11a4ad.png)
您最近一年使用:0次
2023-11-07更新
|
619次组卷
|
5卷引用:河南省焦作市博爱县第一中学2023-2024学年高二上学期期中数学试题
名校
解题方法
2 . 如图,在直三棱柱
中,
,
是面积为
的正方形,且
与平面
所成的角为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/a423e6ce-c2d8-41d2-925e-2ad467b9332d.png?resizew=163)
(1)求三棱柱
的体积;
(2)若
为棱
上靠近
的三等分点,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61dedee1850194d45fb23f52c72da94d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d37f1ae8a2cf694c98fa3afd5b57e435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/a423e6ce-c2d8-41d2-925e-2ad467b9332d.png?resizew=163)
(1)求三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61dedee1850194d45fb23f52c72da94d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211ad5a06b505b8365a62c1946f3cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d1a1b7edecd3344707cf04ea3e86916.png)
您最近一年使用:0次
2023-04-15更新
|
200次组卷
|
2卷引用:河南省商丘市部分学校2022-2023学年高二下学期期中考试数学试题
3 . 阳马,中国古代算数中的一种几何形体,是底面为长方形,两个三角面与底面垂直的四棱锥体.如图,四棱锥P-ABCD就是阳马结构,PD⊥平面ABCD,且
,
,
.
平面
;
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bec03e804f0cea1db5cde2aa185056a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27db558e8db4c957654c8e5cecd2d2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c4336d602211dbca2f1c5fc511f45c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae78e8bb0d1a42759b5464d23d63a601.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877e0b42cc7f2add2521ba2d876af2e4.png)
您最近一年使用:0次
2023-04-13更新
|
1809次组卷
|
5卷引用:河南省许昌市鄢陵县职业教育中心(升学班)2022-2023学年高二下学期期中考试数学试题
河南省许昌市鄢陵县职业教育中心(升学班)2022-2023学年高二下学期期中考试数学试题广西柳州高级中学、南宁市第三中学2023届高三联考数学(文)试题第13章 立体几何初步(B卷·能力提升)-【单元测试】2022-2023学年高一数学分层训练AB卷(苏教版2019必修第二册)广东省肇庆市德庆县香山中学2022-2023学年高一下学期5月月考数学试题(已下线)第六章立体几何初步章末二十种常考题型归类(2)-【帮课堂】(北师大版2019必修第二册)
名校
解题方法
4 . 如图,四边形ABCD是圆柱底面的内接四边形,是圆柱的底面直径,
是圆柱的母线,E是AC与BD的交点,
,
.
(1)记圆柱的体积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737b04ce09bc7e1ed86dc9b3c85203b.png)
(2)设点F在线段AP上,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0724089d732523d6f5d0f0fbc6f64984.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5744f53b3376ffbe7a6bc5044c861273.png)
您最近一年使用:0次
2023-02-23更新
|
6965次组卷
|
15卷引用:河南省安阳市第一中学2023-2024学年高二上学期第二次阶段考试数学试题
河南省安阳市第一中学2023-2024学年高二上学期第二次阶段考试数学试题山西省晋中市平遥县第二中学2022-2023学年高二下学期3月月考数学试题2023届安徽省、云南省、吉林省、黑龙江省高三下学期2月适应性测试数学试题2023年安徽省、云南省、吉林省、黑龙江省联考数学试卷评价(已下线)2023年四省联考变试题17-22云南省2023届高三第一次高中毕业生复习统一检测数学试题山西省大同市2023届高三阶段性模拟(2月联考)数学试题(A卷)(已下线)专题13空间向量与立体几何(解答题)陕西省宝鸡市千阳县中学2023届高三第十二次模考理科数学试题(已下线)专题08 立体几何(理科)(已下线)上海市华东师范大学第二附属中学2023届高三冲刺模拟4数学试题山西省大同市第一中学校等2校2023届高三一模理科数学试题(已下线)江西省九师联盟2024届高三上学期10月联考数学试题广东省深圳市宝安中学2024届高三上学期12月月考数学试题(已下线)第二章 立体几何中的计算 专题一 空间角 微点10 二面角大小的计算综合训练【培优版】
名校
5 . 如图,多面体
中,
平面
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0ae57ea3922dd4d1493a4a8e040995.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/b4fbd5a6-8069-4979-a39e-66b633f7572e.png?resizew=153)
(1)在线段
上是否存在一点
,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
平面
?如果存在,请指出
点位置并证明;如果不存在,请说明理由;
(2)当三棱锥
的体积为8时,求平面
与平面AFC夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8df226cdfaf59a111f778ce07d33d06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee21949feefb980c0d65587ff0497d58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0ae57ea3922dd4d1493a4a8e040995.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/b4fbd5a6-8069-4979-a39e-66b633f7572e.png?resizew=153)
(1)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a0d238b6e9b49bbea22a79402e8e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(2)当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e024a87e5b48bfa241169def613104.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29319a28b4ab8cc3a20f0673fd0c24c0.png)
您最近一年使用:0次
2022-05-31更新
|
1652次组卷
|
5卷引用:河南省焦作市博爱县第一中学2023-2024学年高二上学期期中数学试题
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
|
990次组卷
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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
9 . 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
|
607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
10 . 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