1 . 在梯形
中,
,
是线段
上一点,
,
,
,
,把
沿
折起至
,连接
使得平面
平面
.
平面
;
(2)求异面直线
与
所成的角;
(3)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bdb3995265a321989202ff01001013d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96b08daf5a6880ff23085d10a8b51823.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbfa1a2af7e38d33634c462300df381f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb048f5765a7187c85e304089baf0eb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51600ff4d6e109bf0288b2ea2e7fc92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235d1553f6806c1eee3b17b94d23f0f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6bfad3f7e65188bcf7f62ea5acdbf4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c34b18525831f3eda7bb90be0199b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c2bc5e50b8dfa02601c70822252854a.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e6629d0e1a4ce3fe4f0345f6961473.png)
您最近一年使用:0次
解题方法
2 . 将等腰直角三角形
绕着它的斜边
旋转,当C到达P位置时,
,M是
上的点.
(1)若M是
上的中点,求三棱锥
的体积;
(2)若平面
与平面
的夹角为45°,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cecdc145723d4b18d66934e0fa1593d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/9/761322ef-a07f-4bb6-9a87-b0c57e8ae868.png?resizew=175)
(1)若M是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d90f940f5693b22ddf2e7c761887d8.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf2f0df53aa68c9c334165034788166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2024-01-11更新
|
448次组卷
|
3卷引用:河南省郑州市第十八中学2023-2024学年高二上学期期末模拟数学试题(四)
3 . 如图所示,四边形
是直角梯形
单位:
,求图中阴影部分绕
所在直线旋转一周所成几何体的表面积和体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9e4fea666183ad7f311f188c7ebc54d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/14/6395c7ca-ca82-476b-b9d2-ae2897f373ce.png?resizew=195)
您最近一年使用:0次
4 . 如图是一个奖杯的三视图,试根据奖杯的三视图计算它的表面枳和体积(尺寸如图,单位:cm).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/13/7bf9be8a-b3b3-433c-a06b-0576dec619cf.png?resizew=417)
注:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/13/7bf9be8a-b3b3-433c-a06b-0576dec619cf.png?resizew=417)
注:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9356948217cee1f2e15c92ea98037b02.png)
您最近一年使用:0次
解题方法
5 . 如图,已知正方体
的棱长为4.
(1)求二面角
的正切值;
(2)若E,F分别是棱AD,
的中点,请画出过B,E,F三点的平面与正方体
表面的交线(保留作图痕迹,画出交线,无需说明理由),并求出交线围成的多边形的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/6/feefc466-f451-4cc6-a861-8efd8257dd99.png?resizew=155)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e435c8d07516114af03140faf90c950c.png)
(2)若E,F分别是棱AD,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
您最近一年使用:0次
名校
解题方法
6 . 在三棱锥
中,点D在以AB为直径的半圆弧上,且平面
平面ABC,
,
.
平面BCD;
(2)当三棱锥
的体积取得最大值时,求三棱锥
的表面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf6dc837ae85207789b94d109c5c2eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526908dfb46cf151b8ab1492a9d52047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca5dd496ee0c1170ef6dcc48266ee444.png)
(2)当三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
您最近一年使用:0次
2023-06-26更新
|
347次组卷
|
7卷引用:河南省郑州市新郑市第一中学2022-2023学年高一下学期6月月考数学试题
7 . 在如图所示的几何体中,底面
是正方形,四边形
是直角梯形,
,且四边形
底面
分别为
的中点,
.
(1)求证:平面
平面
;
(2)求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c9854839f8f7fe792cd83cf3aa8b093.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b137f02d1323fe46ce853f662542d2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e675e59fa66ecdf14ba695e5e649222.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0509a2de857dc2589a38686afbb1f6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86a8a140610df89623519116d9e9697c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d15fff0370d17e3befc6e3299820d35.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/5/c028d64c-c99a-4927-b1a8-57419def5b7e.png?resizew=163)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de22059d7d80f24817235269e9bb1ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c9854839f8f7fe792cd83cf3aa8b093.png)
(2)求多面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bab155dd2cd44b7301963056f9b0444b.png)
您最近一年使用:0次
2023-06-22更新
|
623次组卷
|
5卷引用:河南省新郑市第一中学2024届高三上学期12月阶段测试数学试题
8 . 如图1,在梯形
中,
,点E在线段
上,
,将
沿
翻折至
的位置,连接
,点F为
中点,连接
,如图2,
上是否存在一点Q,使平面
平面
?若存在,请确定点Q的位置,若不存在,请说明理由;
(2)当平面
平面
时,求三棱锥
的体积,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c0e114615529829dfb879fd823f081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e73c8c1d2ba6b29b301380a45dfbcdd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e742966e3711cfa53dce04022acf4bcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbe40405cd7bd60d69dd535d6da85c00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acfb204d9e224f1b792b87c54080d957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29eb63c36ca248a27609c059fbc5400a.png)
(2)当平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90d96357a07048ba79b8c84097d359d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6bfad3f7e65188bcf7f62ea5acdbf4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b115316e0fcd2ef46a4dd383472996e4.png)
您最近一年使用:0次
2023-06-22更新
|
898次组卷
|
7卷引用:河南省郑州市新郑市第一中学2022-2023学年高一下学期6月月考数学试题
9 . 如图,在正三棱柱中,
为
上一点,
,
,
为
上一点,三棱锥
的体积为
.
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b3e7c7845a0ec3cbac709fda131764.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a52848aff08399a36f217356007a4b.png)
您最近一年使用:0次
2023-05-27更新
|
1016次组卷
|
5卷引用:河南省郑州市九师联盟2023届高三考前押题卷文科数学试题
河南省郑州市九师联盟2023届高三考前押题卷文科数学试题河南省驻马店市2023届高三三模文科数学试题河南省开封市杞县等4地2022-2023学年高三下学期期末考试文科数学试题江西省南昌市部分学校2023届高三模拟考前押题模拟预测数学(文)试题(已下线)8.6.3平面与平面垂直 (第2课时) -【上好课】(人教A版2019必修第二册)
名校
解题方法
10 . 在直三棱柱
中,E为棱
上一点,
,
,D为棱
上一点.
(1)若
,且D为
靠近B的三等分点,求证:平面
平面
;
(2)若△ABC为等边三角形,且三棱锥
的体积为
,求二面角
的正弦值的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d62d95da5235c7fe783203d8f7c81b64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/28/f7ccf1dd-bc1a-48cf-954d-5f1e2a5138fc.png?resizew=130)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d89ba4036a5d18ec4abed44d7fd8e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b3e7c7845a0ec3cbac709fda131764.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
(2)若△ABC为等边三角形,且三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86f0c01cdd682431365cf43dfba98bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18483c9c195ecd922772527fa85c0fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/920afebdfaec5c13216348a34ac4b03e.png)
您最近一年使用:0次
2023-05-26更新
|
580次组卷
|
4卷引用:河南省郑州市九师联盟2023届高三考前预测押题理科数学试题