名校
解题方法
1 . 如图所示,在四棱锥
中,四边形ABCD为矩形,△PAD为等腰三角形,
,平面PAD⊥平面ABCD,且AB=1,AD=2,E,F分别为PC,BD的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/28/8a00ff3c-982c-4c2a-af98-dd34da2b3ceb.png?resizew=152)
(1)证明:EF∥平面PAD;
(2)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f67538eedbdf54a1bcaff4394230e81.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/28/8a00ff3c-982c-4c2a-af98-dd34da2b3ceb.png?resizew=152)
(1)证明:EF∥平面PAD;
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
您最近一年使用:0次
2023-01-08更新
|
495次组卷
|
2卷引用:吉林省长春市十一高中2022-2023学年高一下学期第二学程考试数学试题
2 . 如果两个球的表面积之比为4∶9,那么这两个球的体积之比为( )
A.8∶27 | B.2∶13 | C.4∶9 | D.2∶9 |
您最近一年使用:0次
名校
解题方法
3 . 如图,在多面体
中,已知四边形
为矩形,
为平行四边形,
平面
的中点为
的中点为
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/18/8dc061d4-9180-4798-9245-18620c1aa04c.png?resizew=181)
(1)求证:
平面
;
(2)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af496393c1559c256ffe2ff67138ef05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f46b357e543eb2e895d0ea4742f4546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de6a4c95a6d856b19dcc8d0cdc37c87c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6e48126cea0b0a3dce466deee97b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f269480b955b85263ac9a350f43fef5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/18/8dc061d4-9180-4798-9245-18620c1aa04c.png?resizew=181)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c979c0206fcbb2442014eed3cfb941e.png)
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名校
解题方法
4 . 如图,半径为
的球的两个内接圆锥有公共的底面,若两个圆锥的体积之和为球的体积的
,则这两个圆锥高之差的绝对值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca8b26c3ad6d892590290a2304126bd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/18/c5fa364b-36e7-453c-945e-eafe4a5b1935.png?resizew=166)
您最近一年使用:0次
2022-12-17更新
|
167次组卷
|
2卷引用:吉林省四平市第一高级中学2019-2020学年高二上学期期中考试数学(文)试题
5 . 如图1,在直角梯形
中,
,点
在
上,且
,将
沿
折起,使得平面
平面
(如图2).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/aed5f2a1-3f02-40bf-837e-52a04809dbc0.png?resizew=360)
(1)求点
到平面
的距离;
(2)在线段
上是否存在点
,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
平面
?若存在,求三棱锥
的体积;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fd9464246dd0171d1120f174b0baec2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377b5f7197e5bd1afeea4d931307956a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d28c625d7ac6878957facc8274d459c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01ff27eea7545bb06f9472f91290c54e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/aed5f2a1-3f02-40bf-837e-52a04809dbc0.png?resizew=360)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
您最近一年使用:0次
2022-12-16更新
|
443次组卷
|
2卷引用:吉林省长春市十一高中2022-2023学年高一下学期第二学程考试数学试题
名校
解题方法
6 . 如图,在正方体
中,E,F是底面正方形
四边上的两个不同的动点,过点
的平面记为
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/be42cb24-a40c-4f8d-af2f-c2e172820934.png?resizew=160)
![](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/0fd191d81c6f35dc5a014872771673c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/be42cb24-a40c-4f8d-af2f-c2e172820934.png?resizew=160)
A.![]() |
B.当E,F分别是![]() ![]() ![]() |
C.当E,F分别是![]() ![]() ![]() |
D.当F是![]() ![]() |
您最近一年使用:0次
2022-12-03更新
|
1594次组卷
|
4卷引用:吉林省吉大附中实验学校2022-2023学年高一下学期期中考试数学试题
名校
解题方法
7 . 如图,在棱长为1的正方体
中,
是棱
上的动点,
是线段
上的动点,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/f068ca5c-9408-4564-8b57-c04b098064e0.png?resizew=137)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/f068ca5c-9408-4564-8b57-c04b098064e0.png?resizew=137)
A.![]() |
B.三棱锥![]() |
C.异面直线![]() ![]() ![]() |
D.直线![]() ![]() ![]() |
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2022-11-16更新
|
523次组卷
|
6卷引用:吉林省吉林市等2地2022-2023学年高二上学期期中联考数学试题
8 . 《乌鸦喝水》是《伊索寓言》中的一个寓言故事,通过讲述一只乌鸦喝水的故事,告诉人们遇到困难要运用智慧、认真思考才能让问题迎刃而解的道理.如图所示,乌鸦想喝水,发现有一个锥形瓶,已知该锥形瓶上面的部分是圆柱体,下面的部分是圆台,瓶口的直径为3cm,瓶底的直径为9cm,瓶口距瓶颈
,瓶颈到水位线的距离和水位线到瓶底的距离均为
.现将1颗石子投入瓶中,发现水位线上移
,当水位线离瓶口不大于
时,乌鸦就能喝到水,则乌鸦共需要投入的石子数量至少是(石子体积均视为一致)( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/5a9a6718-60b1-4a8f-919b-59f7927f98d5.png?resizew=276)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b9355bfefc563dfa1f06e9795ef91bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d656a877d30600a9d023dbbdbe2b4fa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79bb82683d517b97fd2629574340cd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91c6e55bca72a472f3bedf5896d6139b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/17/5a9a6718-60b1-4a8f-919b-59f7927f98d5.png?resizew=276)
A.2颗 | B.3颗 | C.4颗 | D.5颗 |
您最近一年使用:0次
2022-11-13更新
|
291次组卷
|
3卷引用:吉林省辽源市第五中学校2022-2023学年高三上学期期中数学试题
9 . 已知矩形
中,
,
,将
沿
折起至
,当
与
所成角最大时,三棱锥
的体积等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73636989e83905f8800a865c2b608c43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38c430e9f8f14a4753fc8e1da8aeca22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f20e3745b76031e0bf6f5a4a860165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b32ae75c9beabff560f1b52a52d434.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2022-10-31更新
|
343次组卷
|
2卷引用:吉林省长春外国语学校2022-2023学年高三上学期期中考试数学试题
名校
10 . 如图,直三棱柱
内接于高为
的圆柱中,已知
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/14/08a10c66-ec46-4866-ab5c-dd8b88b8779f.png?resizew=136)
(1)求圆柱的表面积;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71f2185273bf04c11118c7954f7ec822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ed8f7d3d7043d4b1eb98fc5c4e2fcd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a67d8576417f761dd5f583ad3a1555a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1799f2f26ed09738aa08fdf64ca86242.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/14/08a10c66-ec46-4866-ab5c-dd8b88b8779f.png?resizew=136)
(1)求圆柱的表面积;
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aeb2af3f9181e6fcce86c71aee45c9e1.png)
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2022-10-11更新
|
1346次组卷
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8卷引用:吉林省白城市通榆县毓才高级中学有限责任公司2023-2024学年高二上学期10月期中数学试题
吉林省白城市通榆县毓才高级中学有限责任公司2023-2024学年高二上学期10月期中数学试题上海市奉贤区2023届高三上学期期中数学试题上海市杨浦区同济大学第一附属中学2024届高三上学期期中数学试题上海市洋泾中学2023届高三上学期10月月考数学试题(已下线)第20讲 空间向量与立体几何-2(已下线)3.4 空间向量在立体几何中的应用(作业)(夯实基础+能力提升)-【教材配套课件+作业】2022-2023学年高二数学精品教学课件(沪教版2020选修第一册)(已下线)重难点01 空间角度和距离五种解题方法-【满分全攻略】2022-2023学年高二数学下学期核心考点+重难点讲练与测试(沪教版2020选修一+选修二)上海市敬业中学2024届高三上学期10月月考数学试题