名校
解题方法
1 . 如图,有一个直径AB等于2的半圆,过点A作这个半圆所在平面的垂线,在垂线上取一点S,使AS=AB,点C为半圆上的一个动点,点M、N分别为A在SB、SC上的射影.当三棱锥
的体积最大时,SC与平面ABC所成角的大小为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5d421ab9e6219769f5e5109e4cfe56.png)
您最近一年使用:0次
2023-01-31更新
|
155次组卷
|
2卷引用:上海市新中高级中学2023-2024学年高二上学期期中数学试题
名校
2 . 已知三棱锥
的四个顶点都在球
的球面上,
,
,
是边长为
的等边三角形,
的面积为
,则球
的体积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c383691e8d740830a865b12d66f7633.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860c4c9419ebfa927b3f3ea14e4f4784.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa37aefb6d45efe4e20ba48c2e7dfa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
您最近一年使用:0次
2023-01-19更新
|
1107次组卷
|
6卷引用:湖北省恩施州高中教育联盟2023-2024学年高二下学期4月期中考试数学试题
20-21高二上·北京·期中
名校
解题方法
3 .
的三边长分别为3、4、5,
为平面
外一点,它到三边的距离都等于2,则
到平面
的距离是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
您最近一年使用:0次
名校
解题方法
4 . 正三棱锥
的侧棱长为
,
为
的中点,且
,则三棱锥
外接球的表面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44abde1eb6e17e06783b0d88c34c8b03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
您最近一年使用:0次
2023-01-11更新
|
1166次组卷
|
5卷引用:浙江省浙北G2联盟2022-2023学年高一下学期4月期中联考数学试题
5 . 如图,已知六棱锥
的底面是正六边形,
平面
,
,给出下列结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/25e5ed55-bdc3-438a-8f88-2061dea26c12.png?resizew=235)
①
;
②直线
平面
;
③平面
平面
;
④直线
与平面
所成角为
;
其中正确的有_______ (把所有正确的序号都填上)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3b7838a53d0b3ed4565fb6a890f365d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9801cabc43c024b9c5fac34b7db5d69b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/15/25e5ed55-bdc3-438a-8f88-2061dea26c12.png?resizew=235)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9104a1941e557a85fd1496bc2b9be297.png)
②直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08f8b463fcecf0a757f386db56e074d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6c2dad46a9052a4185a4f7b4ae8a2e.png)
③平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e6c2dad46a9052a4185a4f7b4ae8a2e.png)
④直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
其中正确的有
您最近一年使用:0次
解题方法
6 . 在正三棱柱
中,
,点
满足
,其中
,给出下列结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/1bda5045-a264-4bb5-a64d-6dadc06a56af.png?resizew=165)
①当
时,
的周长为定值;
②当
时,三棱锥
的体积为定值;
③当
时,有且仅有一个点
,使得
;
④若
,则点
的轨迹所围成的面积为
.
其中正确的结论是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0e44cb429eea46e7ee4320147192b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac6b545127bd51036a5a7b0d3cd5b320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c88a4bc86ffd96234a9b3a0ca1aab275.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/5/1bda5045-a264-4bb5-a64d-6dadc06a56af.png?resizew=165)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d68f2678989a5ce7431cfd51b019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b13e4828c0b33a84f8b97828a6bde9f.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2753dc1c83d54044b89e628a7eb247f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aab98011d732d4094e4e881b0bd2bd6.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3cf0f585938ede9eca890a6eb326d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2b1e3ac6ea9deecc8f2575c1d3bfd09.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b880beefbff325ba166fca1dcf7f03c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c487fec20bd809e0baf5cb39afe8979.png)
其中正确的结论是
您最近一年使用:0次
2022-12-04更新
|
492次组卷
|
4卷引用:上海外国语大学附属浦东外国语学校2023-2024学年高二上学期期中考试数学试卷
上海外国语大学附属浦东外国语学校2023-2024学年高二上学期期中考试数学试卷北京市第五十七中学2023届高三上学期12月月考数学试题(已下线)北京市西城区2022届高三二模数学试题变式题11-15(已下线)第三章 空间轨迹问题 专题四 立体几何轨迹面积、体积问题 微点2 立体几何轨迹面积、体积问题综合训练【培优版】
名校
7 . 正方体
的棱长为1,点P是
内不包括边界的动点,若
,则线段AP长度的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de60f6ffd5ab327d4cfe32d26d95da70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55e1de129bfc451f4c7160cc50666ad8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/73e405f4-7977-479b-b2f9-8e6a26dd00b9.png?resizew=170)
您最近一年使用:0次
2022-11-30更新
|
1036次组卷
|
4卷引用:安徽省六安第一中学2022-2023学年高一下学期期中考试数学试题
解题方法
8 . 如图,在梯形ABCD中,
,
,
,
,将
沿对角线BD折起,设折起后点
的位置为
,并且平面
平面BCD.则下面四个命题中正确的是______ .(把正确命题的序号都填上)
①
;②三棱锥
的体积为
;③
;④平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4adf90a8c2b29334cdc5aa5b554991f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5679a74e9f5506266ab627894ab03243.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/386c7de62e8f9a8161ebaefe6b4ec35e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe052786101dfcc941480919eb2cecc.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95b78d94be9cf126522b58204b320bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb4c6e9a723aa843e6ba62d7c1a3a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97eea5144ef3750d3b75c86a008319aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53d138354c4e021ac8ae2a2fb176ca14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff8c968d4a1798957d5134b45f5049d0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/c2c25ad4-4d3a-419b-a3a4-57b0c220b229.png?resizew=312)
您最近一年使用:0次
名校
9 . 如图,已知四棱锥
的底面是边长为2的菱形,且
,
,
平面ABCD,F,O分别是PA,BD的中点,E是线段PB上的动点,给出下列四个结论:
①
;②
;③直线PO与底面ABCD所成角的正弦值为
;④
面积的取值范围是
.______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72d4f1b71eb0a8d8211757ec96d0d7e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4c15fb8fc3239d45bd4e7d8971f58e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8066f2f5e880d2217bc7f576920aaf69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45978875144e212f1ca6fa4a77ad648c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80651f797ab9dccfd7163c605b091ad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac97e7582374a782ceb4c5a95cbc8ffe.png)
您最近一年使用:0次
解题方法
10 . 如图,在正方体ABCD﹣A1B1C1D1中,AB=2,则直线AA1到平面BB1D1D的距离为______ .
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/1c04097b-67ad-4801-82bd-c8417b6e4560.png?resizew=143)
您最近一年使用:0次
2022-11-21更新
|
367次组卷
|
6卷引用:上海市华东师范大学附属枫泾中学2021-2022学年高二上学期期中数学试题
上海市华东师范大学附属枫泾中学2021-2022学年高二上学期期中数学试题上海市上南中学2023-2024学年高二上学期期中数学试题(已下线)第01讲 空间直线与平面(核心考点讲与练)(2)(已下线)上海高二上学期期中【夯实基础60题考点专练】(2)(已下线)第八章立体几何初步章末题型大总结(精讲)(3)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)(已下线)8.6.2 直线与平面垂直(精讲)