名校
解题方法
1 . 如图,在三棱锥
中,三条侧棱OA,OB,OC两两垂直,且
,M为
内部一动点,过M分别作平面OAB,平面OBC,平面OAC的垂线,垂足分别为P,Q,R.
![](https://img.xkw.com/dksih/QBM/2022/5/7/2974506010230784/2975624099708928/STEM/2b11d325-7f6d-4c17-85a9-065fc761d527.png?resizew=271)
①直线PR与直线BC是异面直线;
②
为定值;
③三棱锥
的外接球表面积的最小值为
;
④当
时,平面PQR与平面OBC所成的锐二面角为45°.
则以上结论中所有正确结论的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbab39da847da8a559994b6c6004aa60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://img.xkw.com/dksih/QBM/2022/5/7/2974506010230784/2975624099708928/STEM/2b11d325-7f6d-4c17-85a9-065fc761d527.png?resizew=271)
①直线PR与直线BC是异面直线;
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b4389530f4d31bc0ae46d0edfcdd2dd.png)
③三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64bab74dadb5557a3762947e52feb532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4966e5af166b69a0a38a98abf555b6b.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38db6f3badb51bef6fa220ce110af854.png)
则以上结论中所有正确结论的序号是
您最近一年使用:0次
2022-05-09更新
|
514次组卷
|
3卷引用:四川省南充市2022届高三下学期高考适应性考试(三诊)数学(理)试题
名校
2 . 如图,直二面角的棱上有A,B两点,直线
分别在这个二面角的两个半平面内,且都垂直于
.已知
,则
的长为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3c032441543354c154ee67d744abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e190c04954633038f562e631486072.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/2022/4/24/2965231434539008/2967845999673344/STEM/7f9b5f7f-ba63-48a9-869e-00e1be15c711.png?resizew=176)
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2022-04-28更新
|
832次组卷
|
5卷引用:四川省成都市蒲江县蒲江中学2021-2022学年高二下学期5月月考数学(理)试题
解题方法
3 . 三棱锥D-ABC中,△BCD是边长为2的正三角形,△BCD与△ABC所在平面互相垂直,且AC=1,
.则AD=___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
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2022-03-29更新
|
158次组卷
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2卷引用:四川省巴中市恩阳区2020-2021学年高二上学期期末考试数学(文)试题
解题方法
4 . 如图,矩形
中,
,
为边
的中点,将
沿
翻折成
,若
为线段
的中点,则在翻折过程中,下列说法正确的是______ .
①翻折到某个位置,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642e15f06c38176c827db801333153d2.png)
②翻折到某个位置,使得
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
③四棱锥
体积的最大值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821309f088a175c00dc0f4828334503d.png)
④点M在某个球面上运动
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80f51c31583fea58fde645474d60b8a.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/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa2a83fed9bf4cb09d84a980452e346.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
①翻折到某个位置,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642e15f06c38176c827db801333153d2.png)
②翻折到某个位置,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
③四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56277d9344bcdcc5a500817d3f0fc0bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821309f088a175c00dc0f4828334503d.png)
④点M在某个球面上运动
![](https://img.xkw.com/dksih/QBM/2022/2/28/2926022268985344/2931320221704192/STEM/08e27024-2fb6-47ba-a42f-c110616649d1.png?resizew=211)
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2022-03-07更新
|
628次组卷
|
3卷引用:四川省德阳市2022届高三第二次质量监测考试文科数学试题
四川省德阳市2022届高三第二次质量监测考试文科数学试题四川省德阳市2022届高三质量监测考试(二)数学(理)试题(已下线)专题5.2 模拟卷(2)-2022年高考数学大数据精选模拟卷(新高考地区专用)
名校
5 . 在边长为6的菱形ABCD中,
,现将
沿BD折起,当三棱锥
的体积最大时,三棱锥
的外接球的表面积为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3a059203f65774fd8f321faa9e8041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
您最近一年使用:0次
2022-03-05更新
|
1410次组卷
|
6卷引用:四川省达州外国语学校2023-2024学年高二上学期9月月考数学试题
四川省达州外国语学校2023-2024学年高二上学期9月月考数学试题山东省济宁市2022届高三一模数学(3月)试题山西省朔州市怀仁市第一中学2022届高三下学期第二次模拟数学(理)试题广东省汕头市潮南区陈店实验学校2021-2022学年高二下学期第一次月考数学试题(已下线)押新高考第16题 空间几何体-备战2022年高考数学临考题号押题(新高考专用)(已下线)“8+4+4”小题强化训练(14)
名校
解题方法
6 . 如图,已知矩形ABCD,
,
,
平面ABCD,且
,点E为线段DC(除端点外)上的一点,沿直线AE将
向上翻折成
,M为
的中点,则下列结论正确的有______ .(写出所有正确结论的序号)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/c3d79f87-1750-41ea-91bd-7e207308f8e4.png?resizew=211)
①三棱锥
的体积为
;
②当点E固定在线段DC某位置时,则
在某圆上运动;
③当点E在线段DC上运动时,则
在某球面上运动;
④当点E在线段DC上运动时,三棱锥
的体积的最小值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a22d6b860f06fe23618b0d3de6768fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae341f580ff8fbf21f616fe900b0e4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63b43490ca09467a4c8cd8cfe91c94e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f9c64303370347131dd9d8c5c70c01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b435d7fc33860ae191f9111d880b40.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/c3d79f87-1750-41ea-91bd-7e207308f8e4.png?resizew=211)
①三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f26712d1a7a5864cd18498f16f7bd96c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edb57d84f9bbcb3e30d4ce7e2e1e8604.png)
②当点E固定在线段DC某位置时,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
③当点E在线段DC上运动时,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
④当点E在线段DC上运动时,三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab71ff19bd011f08cc4d379dde1b6eab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5040d31e784398842b04ed7dd0aacc10.png)
您最近一年使用:0次
解题方法
7 . 如图,AB是
的直径,PA垂直于
所在的平面,C是圆周上不同于A,B的任意一点,
,三棱锥P-ABC体积的最大值为
,则当△PBC的面积最大时,线段AC的长度为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31571febbf2af2957fab1a173f5fcf12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a391005600bdd69c96750589f9adb048.png)
![](https://img.xkw.com/dksih/QBM/2022/1/12/2892757150048256/2915707766153216/STEM/f31acdf62d724f74834099acebf268b0.png?resizew=156)
您最近一年使用:0次
2022-02-13更新
|
398次组卷
|
4卷引用:四川省遂宁市2021-2022学年高三上学期第一次诊断性考试数学(理)试题
名校
8 . 如图,二面角
等于
,A、
是棱l上两点,BD、AC分别在半平面
、
内,
,
,且
,则CD的长等于________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4526c88c6844a5ffe389e54c60d48981.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c638fb895acd987140d0ca6bef097499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb0a2d7d40a6c0bf1fddb802db381689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6a28db73337057c7741272c5fb22e3e.png)
![](https://img.xkw.com/dksih/QBM/2021/12/24/2879529172525056/2912184699314176/STEM/571865b7-ffa3-43e2-a718-f1846ac6692e.png?resizew=188)
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2022-02-08更新
|
1987次组卷
|
12卷引用:四川省泸州市泸县泸县第四中学2022-2023学年高一下学期期末数学试题
四川省泸州市泸县泸县第四中学2022-2023学年高一下学期期末数学试题四川省达州市宣汉县土黄中学2023-2024学年高二上学期第三次月考数学试题安徽省合肥市第八中学2021-2022学年高二上学期段考(三)文科数学试题浙江省精诚联盟2021-2022学年高二下学期3月联考数学试题湖南师范大学附属中学2021-2022学年高一下学期期末数学试题(已下线)第1讲 空间向量及其运算 (2)江苏省南京市第二十九中学2022-2023学年高一下学期5月月考数学试题(已下线)第04讲 空间向量及其运算 (2)福建省将乐县第一中学2022-2023学年高一下学期第三次月考数学试题福建省厦门第二中学2023-2024学年高二上学期第一次月考(9月)数学试题福建省福州市闽侯县第一中学2023-2024学年高二上学期10月月考数学试题广东省肇庆鼎湖中学2023-2024学年高二上学期10月月考数学试题
9 . 如图,在正方体
中,点M,N分别为棱
,CD上的动点(包含端点),则下列说法正确的是______ .
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/12/2a1cc35e-2144-448b-a284-d8d7bd67e168.png?resizew=181)
①当M为棱
的中点时,则在棱CD上存在点N使得
;
②当M,N分别为棱
,CD的中点时,则在正方体中存在棱与平面
平行;
③当M,N分别为棱
,CD的中点时,则过
,M,N三点作正方体的截面,所得截面为五边形;
④若正方体的棱长为2,点
到平面
的距离最大值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/12/2a1cc35e-2144-448b-a284-d8d7bd67e168.png?resizew=181)
①当M为棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66fae8e33cd86fa8dab72704eaafe1ba.png)
②当M,N分别为棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e74395b07e8153a0ef0bbcb5881013f.png)
③当M,N分别为棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
④若正方体的棱长为2,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6795cae2df43a722e1355e9562d93c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e74395b07e8153a0ef0bbcb5881013f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
您最近一年使用:0次
名校
解题方法
10 . 如图,在正方体
中,E是线段
上的动点,下列四个结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/4ead815c-884c-4204-ae02-ea6ae784984b.png?resizew=164)
①
面
;
②
面
;
③二面角
的平面角为
;
④三棱锥
的体积不变.
其中正确结论的序号为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/4ead815c-884c-4204-ae02-ea6ae784984b.png?resizew=164)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d850305485a6d3ee30fe313dc8bb736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/565133e91e3ace2b2187cfc6f1db5be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
③二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc741de0ca651a0f3ef1974c3bb52bb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
④三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96a91c2d02c8116e99111c488056553d.png)
其中正确结论的序号为
您最近一年使用:0次
2022-01-25更新
|
228次组卷
|
2卷引用:四川省眉山市2021-2022学年高二上学期期末数学(文)试题