名校
1 . 如图,已知四棱锥
的底面
是边长为2的正方形,
底面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/482696e5-73b1-4e77-8700-17e020954aeb.png?resizew=172)
(1)求直线
与平面
所成的角的大小;
(2)求四棱锥
的侧面积.
![](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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bec03e804f0cea1db5cde2aa185056a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/482696e5-73b1-4e77-8700-17e020954aeb.png?resizew=172)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
2019-11-06更新
|
383次组卷
|
4卷引用:上海市第二中学2018-2019学年度高二下学期期末数学试题
2 . 如图,已知长方体
中,
,
,点
为
中点,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/6f6b9da4-bd71-4eab-9be9-3575a6003d0f.jpg?resizew=139)
(1)求直线
与平面
所成角的大小;
(2)求异面直线
与
所成角大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0de7e1ab7c0aae3e54766b75516787f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b3f142ddf3f82a4588012c7d8692e57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4c783bab7586f60dc14d4f10b6d5b12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d05533a1de2a2d4ab2c5e694c90a9a78.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/6/6f6b9da4-bd71-4eab-9be9-3575a6003d0f.jpg?resizew=139)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cafd67f44a30e27db130e90ce1823fc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94aad4c2109f60fcbf5488a545b16c6c.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3acfd91be9979f627c48a059dd2e2b1.png)
您最近一年使用:0次
3 . 如图(1).在
中,
,
,
,
、
分别是
、
上的点,且
,将
沿
折起到
的位置,使
,如图(2).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/08f9eacc-03f7-495b-8cb6-f16985a35f7d.png?resizew=298)
(1)求证:
平面
;
(2)当点
在何处时,三棱锥
体积最大,并求出最大值;
(3)当三棱锥
体积最大时,求
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87fd28b8b2bde9de5630a6106a6f762e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1682d306c38087d9e6f7efb9cec596a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82957366f4c9272b6ee99126d4b6bf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f460edcced5597615113c0fdc95b1dfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f07107087ce4abdfa5fc68fe6fb62f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fffbf41f3890efb6956907ad3c4062a0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/08f9eacc-03f7-495b-8cb6-f16985a35f7d.png?resizew=298)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a148a5584e41408fc74f8bd386b5b8.png)
(2)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db4c18aba9681a8475968248764d4c3a.png)
(3)当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db4c18aba9681a8475968248764d4c3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
您最近一年使用:0次
4 . 如图所示,某地出土的一种“钉”是由四条线段组成,其结构能使它任意抛至水平面后,总有一端所在的直线竖直向上.并记组成该“钉”的四条等长的线段公共点为
,钉尖为
.
![](https://img.xkw.com/dksih/QBM/2019/8/21/2273588487520256/2273636012761088/STEM/805651fb-5927-46d4-b854-40b0fd2e9ccb.png)
(1)判断四面体
的形状,并说明理由;
(2)设
,当
在同一水平面内时,求
与平面
所成角的大小(结果用反三角函数值表示);
(3)若该“钉”着地后的四个线段根据需要可以调节与底面成角的大小,且保持三个线段与底面成角相同,若
,
,问
为何值时,
的体积最大,并求出最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02cebb466d8642424bd583e8843ffe39.png)
![](https://img.xkw.com/dksih/QBM/2019/8/21/2273588487520256/2273636012761088/STEM/805651fb-5927-46d4-b854-40b0fd2e9ccb.png)
(1)判断四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceb9e0ac9f76900e254817c8177ac7f9.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b1928def070e2f92b5351f55fbe8eda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fa157b4f65f3a9aa1f7f82de02e99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4195334905e2f190f958dbf5951456f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fa6e3afb5196decc6f087cbfe40cf8a.png)
(3)若该“钉”着地后的四个线段根据需要可以调节与底面成角的大小,且保持三个线段与底面成角相同,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66b31bf4e2816798aa17735cb329f1b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b1928def070e2f92b5351f55fbe8eda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/625164153d89f3f6993a9af173f693e5.png)
您最近一年使用:0次
5 . 如图,在长方体
中,已知
,
,
为棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/0cff17a6-3a0d-4b50-b057-08afbcc6ed33.png?resizew=123)
(1)求四棱锥
的体积;
(2)求直线
与平面
所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b37750daa8ba3b3fe3e9e2092f81c848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa203719e01b3755a5d149191f9e3f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/0cff17a6-3a0d-4b50-b057-08afbcc6ed33.png?resizew=123)
(1)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4117625867a74cd022584500c76deca.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
您最近一年使用:0次
2019-08-17更新
|
572次组卷
|
2卷引用:上海市上海大学附属嘉定高级中学2022-2023学年高一下学期期末数学试题
名校
6 . 如图,等高的正三棱锥P-ABC与圆锥SO的底面都在平面M上,且圆O过点A,又圆O的直径AD⊥BC,垂足为E,设圆锥SO的底面半径为1,圆锥体积为
.
![](https://img.xkw.com/dksih/QBM/2019/6/14/2225517714186240/2225597171228672/STEM/82a96e76567b4323a6b7c5854cb497b0.png?resizew=296)
(1)求圆锥的侧面积;
(2)求异面直线AB与SD所成角的大小;
(3)若平行于平面M的一个平面N截得三棱锥与圆锥的截面面积之比为
,求三棱锥的侧棱PA与底面ABC所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef5d2f9b48d6089c071cca7967792c3c.png)
![](https://img.xkw.com/dksih/QBM/2019/6/14/2225517714186240/2225597171228672/STEM/82a96e76567b4323a6b7c5854cb497b0.png?resizew=296)
(1)求圆锥的侧面积;
(2)求异面直线AB与SD所成角的大小;
(3)若平行于平面M的一个平面N截得三棱锥与圆锥的截面面积之比为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39fccdaf2a6ab6e5e8fad099c1643b38.png)
您最近一年使用:0次
2019-06-14更新
|
415次组卷
|
5卷引用:上海市2018-2019学年高二下学期期末考试复习卷数学试题
名校
7 . 如图,已知
为四面体
内一点,且满足:点
与四面体任一顶点的连线均垂直其余三个顶点所确定的平面,设
.
(1)求证:
;
(2)若
,求证:
,为正四面体,并求直线
与平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495fbf56b3023539b59f7bcee29acc70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b87ab627bd3d7b2d1d8b10c2726b69eb.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e905539588cd8f1521b7ac5d29537efe.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7a6895c0c96685ef5388bfa22c8868c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495fbf56b3023539b59f7bcee29acc70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c76916c6ff302cf4fb4b6ace5bb3a95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58650c0df1400996eadc8969ea7ad749.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/5/4d4b6adf-7544-4192-8a64-abbac88922ac.png?resizew=197)
您最近一年使用:0次
8 . 在四棱锥P-ABCD中,底面ABCD是矩形,PA⊥平面ABCD,
,
,
以AC的中点O为球心,AC为直径的球面交PD于点M,交PC于点N.
![](https://img.xkw.com/dksih/QBM/2018/7/6/1982717610647552/1983425373192193/STEM/90076e6eb77549a6ad4aba8aa0f9b9fe.png?resizew=141)
(1)求证:平面ABM⊥平面PCD;
(2)求直线CD与平面ACM所成角的大小;
(3)求点N到平面ACM的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c2753753faf2cb9a0003aa8e3945159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
以AC的中点O为球心,AC为直径的球面交PD于点M,交PC于点N.
![](https://img.xkw.com/dksih/QBM/2018/7/6/1982717610647552/1983425373192193/STEM/90076e6eb77549a6ad4aba8aa0f9b9fe.png?resizew=141)
(1)求证:平面ABM⊥平面PCD;
(2)求直线CD与平面ACM所成角的大小;
(3)求点N到平面ACM的距离.
您最近一年使用:0次
名校
9 . 已知圆锥
的底面半径为2,母线长为
,点
为圆锥底面圆周上的一点,
为
圆心,
是
的中点,且
.
(1)求圆锥的全面积;
(2)求直线
与平面
所成角的大小.
(结果用反三角函数值表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60cbb271baca5cd015f30e07d9eebfd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
圆心,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b895d317c1f6a38bb2337ab6e4803008.png)
(1)求圆锥的全面积;
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
(结果用反三角函数值表示)
![](https://img.xkw.com/dksih/QBM/2018/4/19/1927583351160832/1930349183631360/STEM/d0884b076c1e43a4a357df24610ee418.png?resizew=132)
您最近一年使用:0次
2018-04-23更新
|
318次组卷
|
3卷引用:上海市徐汇区2020-2021学年高二下学期期末数学试题
10 . 如图,直三棱柱
的底面为直角三角形,两直角边AB和AC的长分别为4和2,侧棱
的长为5.
(1)求三棱柱
的体积;
(2)设M是BC中点,求直线
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/2777840758e70e7dbbc18cef8f3d6d2b.png)
(1)求三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
(2)设M是BC中点,求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://img.xkw.com/dksih/QBM/2018/3/26/1910453096235008/1912144809205760/STEM/fcea39a5-6aab-4550-9b75-9c122c91768c.png?resizew=201)
您最近一年使用:0次
2018-03-28更新
|
2251次组卷
|
7卷引用:上海市浦东新区川沙中学2018-2019学年高二下学期期末数学试题
上海市浦东新区川沙中学2018-2019学年高二下学期期末数学试题上海市金山区亭林中学2020-2021学年高二下学期期末数学试题2017年普通高等学校招生统一考试数学(上海卷)上海市上海师范大学第二附属中学2021届高三下学期3月月考数学试题(已下线)考向22 空间几何体-备战2022年高考数学一轮复习考点微专题(上海专用)(已下线)重组卷03(已下线)专题23 立体几何解答题(文科)-2