1 . 如图,在棱长为1的正方体
中,
,
分别为棱
,
的中点,
为线段
上一个动点,则( )
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/11/f788475a-4a39-4578-878c-65084fbf45bd.png?resizew=166)
A.![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() |
C.直线![]() ![]() ![]() |
D.若点![]() ![]() ![]() ![]() ![]() ![]() |
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解题方法
2 . 如图所示,该几何体由一个直三棱柱
和一个四棱锥
组成,
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89a7ad15b77c2cc409bc24adff155819.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78f535e16e0474f1660d7d0816ee2318.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/16/b60590fa-533c-4e7e-9389-4347388cc73f.jpg?resizew=113)
A.若![]() ![]() |
B.若平面![]() ![]() ![]() |
C.三棱柱![]() ![]() |
D.当该几何体有外接球时,点![]() ![]() ![]() |
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2023-06-22更新
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1275次组卷
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8卷引用:湖北省武昌实验中学2023-2024学年高三上学期10月月考数学试题
2023高三·全国·专题练习
名校
解题方法
3 . 已知正四棱锥
的体积为
,底面
的面积为
,点
、
分别为
、
的中点,点
为
的靠近点
的三等分点,过点
、
、
的平面将该四棱锥分成上、下两部分,截面形状为四边形,则该四边形的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/492b6d3883713fcaa8a4fdd87b87b480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b837fd9c52f60bfb3b6852733abc790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 在四棱锥
中,底面ABCD是矩形,
,
,平面
平面ABCD,点M在线段PC上运动(不含端点),则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a88c44f558705de3bcefcfc0ece96b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790fc4aac4c77e07f3a2fdcae94646f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
A.存在点M使得![]() |
B.四棱锥![]() ![]() |
C.直线PC与直线AD所成角为![]() |
D.当动点M到直线BD的距离最小时,过点A,D,M作截面交PB于点N,则四棱锥![]() ![]() |
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2023-05-11更新
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3086次组卷
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9卷引用:湖北省黄冈市浠水县第一中学2023届高三下学期5月五模数学试题
湖北省黄冈市浠水县第一中学2023届高三下学期5月五模数学试题湖南省长沙市长郡中学、长沙一中、雅礼中学、湖南师大附中2023届高三下学期5月“一起考”数学试题(已下线)期末考试仿真模拟试卷02-(苏教版2019必修第二册)浙江省金华第一中学2022-2023学年高二下学期6月月考数学试题(已下线)专题09 立体几何初步四川省射洪中学2022-2023学年高一下学期(强基班)第三次月考数学试题四川省宜宾市叙州区第二中学校2023-2024学年高二上学期期中数学试题(已下线)2024届数学新高考Ⅰ卷精准模拟(四)福建省莆田市华侨中学2024届高三上学期第四次月考数学试题
名校
解题方法
5 . 在
中,
,
,
,
为
中点,若将
沿着直线
翻折至
,使得四面体
的外接球半径为
,则直线
与平面
所成角的正弦值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f289ef19c7418a898ea18747aa76e783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f67985b822b482f804d56d5df049f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18743c8af72b34469648451f095fe170.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81b32ae75c9beabff560f1b52a52d434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0f0ccc8492a0ccf1eee24867060643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-05-10更新
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1424次组卷
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5卷引用:湖北省武汉市5G联合体2022-2023学年高一下学期期末联考数学试题
名校
6 . 阅读数学材料:“设
为多面体
的一个顶点,定义多面体
在点
处的离散曲率为
,其中
为多面体
的所有与点
相邻的顶点,且平面
,平面
,平面
和平面
为多面体
的所有以
为公共点的面."解答问题:已知在直四棱柱
中,底面
为菱形,
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495f0476ea52d21c429f7fe732bc12d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20559c2fce92126341420a8170dacc2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/183f3fdb3204864ff2f60c8c1dac2f2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d460b981c22f37c1f73281d83686be92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9d7f18c3c9dae7e6d4f2e96281289f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f733e19f18ab01a3c022331805ed58a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](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/eeed487430a5b8a330f2d0c52166521a.png)
A.直四棱柱![]() |
B.若![]() ![]() ![]() ![]() |
C.若四面体![]() ![]() ![]() ![]() ![]() |
D.若直四棱柱![]() ![]() ![]() ![]() ![]() ![]() |
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2023-05-04更新
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6卷引用:湖北省荆门市龙泉中学、荆州中学·、宜昌一中三校2023届高三下学期5月联考数学试题
湖北省荆门市龙泉中学、荆州中学·、宜昌一中三校2023届高三下学期5月联考数学试题湖南省岳阳市岳阳县第一中学2022-2023学年高一下学期期末数学试题广东省东莞市第七高级中学2022-2023学年高一下学期5月月考数学试题湖南省怀化市雅礼实验学校2023-2024学年高二上学期入学考试数学试题(已下线)第五篇 向量与几何 专题21 曲率与曲率圆 微点3 曲率与曲率圆综合训练(已下线)第六章 突破立体几何创新问题 专题一 跨学科交汇问题 微点3 跨学科交汇问题综合训练【培优版】
7 . 已知三棱锥
的底面ABC是等边三角形,平面SAC⊥平面ABC,
,M为SB上一点,且
.设三棱锥
外接球球心为O,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7c7f81b06e3483428388bacc5e2d74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed46a014ece6a0830c7c8b8deb2c56e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
A.直线OM⊥平面SAC,OA⊥SB | B.直线![]() ![]() |
C.直线OM⊥平面SAC,平面OAM⊥平面SBC | D.直线![]() ![]() |
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2023-04-27更新
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1389次组卷
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4卷引用:湖北省2023届高三一模数学试题
湖北省2023届高三一模数学试题2023年高三黑白卷数学试卷(新高考)(白卷)(已下线)10.4 平面与平面间的位置关系(第1课时)(七大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020必修第三册)(已下线)专题6-1立体几何动点与外接球归类-2
名校
解题方法
8 . 在正四棱柱
中,
,
,
为
中点,
为正四棱柱表面上一点,且
,则点
的轨迹的长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34dca4e1f373b758b5963db675def224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
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5卷引用:湖北省荆州市松滋市第一中学2024届高三上学期迎一检模拟检测(三)数学试题
湖北省荆州市松滋市第一中学2024届高三上学期迎一检模拟检测(三)数学试题广西壮族自治区玉林市2023届高三三模数学(理)试题安徽省定远中学2023届高三下学期高考冲刺卷(一)数学试卷(已下线)重难点突破05 求曲线的轨迹方程(十大题型)-2(已下线)第三章 空间轨迹问题 专题二 立体几何中位置关系类动点轨迹问题 微点1 立体几何中位置关系类动点轨迹问题【培优版】
9 . 在棱长为2的正方体
中,
为
中点,
为四边形
内一点(含边界),若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd94d3c3765c52e2d6375f1959686430.png)
平面
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4da530384dd04ac90a025385e8b3c2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd94d3c3765c52e2d6375f1959686430.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f239fbcc58fc15535db4b5084c4f7253.png)
A.![]() | B.三棱锥![]() ![]() |
C.线段![]() ![]() | D.![]() ![]() |
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2023-03-09更新
|
1600次组卷
|
4卷引用:湖北省八市2023届高三下学期3月联考数学试题
名校
解题方法
10 . 已知正方体
的所有顶点均在体积为
的球O上,则该正方体的棱长为___________ ,若动点P在四边形
内运动,且满足直线
与直线
所成角的正弦值为
,则
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bea86620b6ce1284536813e1a74837.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f645d4b09fba53f971172cd2602c691.png)
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