1 . 如图,在长方体
中,
,点
为线段
上一动点,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/13/89ddf716-573a-4a44-833f-4a97371c9596.png?resizew=166)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fb6e2961e2700947a800a500f60a834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/13/89ddf716-573a-4a44-833f-4a97371c9596.png?resizew=166)
A.直线![]() ![]() |
B.三棱锥![]() ![]() |
C.三棱锥![]() ![]() |
D.直线![]() ![]() ![]() |
您最近一年使用:0次
2 . 把底面为椭圆且母线与底面垂直的柱体称为“椭圆柱”.如图,椭圆柱
中底面长轴
,短轴长
为下底面椭圆的左右焦点,
为上底面椭圆的右焦点,
为
上的动点,
为
上的动点,
为过点
的下底面的一条动弦(不与
重合).
为
的中点时,
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ce50ba5e349425274f05d46d120a74.png)
(2)若点
是下底面椭圆上的动点,
是点
在上底面的投影,且
与下底面所成的角分别为
,试求出
的取值范围.
(3)求三棱锥
的体积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a171cc0cc99f030004562afbbc076d31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd017ff847f31f37593d9c864fc1f12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d8b20bcb61ee074d884ef80a3c4a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d91906f65d3c6ce459c1f1efb93363b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb0628cecbfc98d390e5447d52414e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f555e56d727bcfe7c456a58883c5b8a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22ce50ba5e349425274f05d46d120a74.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a42da28be159399514cc6179a96e34b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50de09eab1f2599073e4f97b89a6e80e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89c79fc0cb461a911eb17f7d49f9f117.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64297d81fb65426718be766c90c74cfc.png)
您最近一年使用:0次
2023-12-30更新
|
907次组卷
|
4卷引用:上海市上海外国语大学附属外国语学校松江云间中学、进才中学、交大附中嘉定分校、复旦附中青浦分校2023-2024学年高二上学期四校联考数学试卷
上海市上海外国语大学附属外国语学校松江云间中学、进才中学、交大附中嘉定分校、复旦附中青浦分校2023-2024学年高二上学期四校联考数学试卷重庆缙云教育联盟2024届高三高考第一次诊断性检测数学试卷广东省惠州市第一中学2024届高三上学期第四次阶段测试数学试题(已下线)第二章 立体几何中的计算 专题七 空间范围与最值问题 微点4 面积、体积的范围与最值问题(二)【基础版】
名校
3 . 如图,在棱长为
的正方体
中,点
在线段
(不包含端点)上,则下列结论正确的有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/12/f5915e45-9e0d-4933-814d-aea18097ff37.png?resizew=164)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](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/0f1f229274a6e17977cc047814212589.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/12/f5915e45-9e0d-4933-814d-aea18097ff37.png?resizew=164)
A.点![]() ![]() ![]() |
B.直线![]() ![]() |
C.异面直线![]() ![]() ![]() |
D.三棱锥![]() ![]() |
您最近一年使用:0次
2023-12-12更新
|
248次组卷
|
2卷引用:广东省佛山市顺德区华侨中学2024届高三上学期12月月考数学试题
解题方法
4 . 如图所示,正方体
中,
,点
在侧面
及其边界上运动,并且总是保持
,则以下四个结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/366daca6-f35e-412a-b0ee-fb2a1fcfb6a8.png?resizew=161)
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bbcdb9f641a2b3e06e0a01c79420667.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/366daca6-f35e-412a-b0ee-fb2a1fcfb6a8.png?resizew=161)
A.![]() | B.![]() |
C.点![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
解题方法
5 . 已知边长为2的等边
,点D、E分别是边
、
上的点,满足
且
,将
沿直线
折到
的位置,在翻折过程中,下列结论成立的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/5/2e407ece-27a3-49d8-a85e-2f3227b8d435.png?resizew=167)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e210c9698063925ad2df6b6c1749571.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f618b39b289e5f3a9efdd60febdc5650.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/34dbf33492e5223df78dea34a24ae015.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/5/2e407ece-27a3-49d8-a85e-2f3227b8d435.png?resizew=167)
A.![]() ![]() |
B.在边![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.存在![]() ![]() ![]() |
您最近一年使用:0次
解题方法
6 . 已知四棱锥
中,底面
是边长为2的正方形,
平面
,
,且以
为圆心、
为半径的圆分别交
,
于
,
两点,点
是劣弧
上的动点,其中
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e124a392dc84fcc1662fe6d896aa12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c9ac405301d3c27523ee19ba415315.png)
A.弧![]() ![]() ![]() ![]() ![]() |
B.弧![]() ![]() ![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-11-28更新
|
244次组卷
|
2卷引用:山东省潍坊市部分市区2023-2024学年高二上学期期中质量监测数学试题
7 . 如图,四棱锥
的底面
是正方形,且平面
平面
.
,
分别是
,
的中点,经过
,
,
三点的平面与棱
交于点
,平面
平面
,直线
与直线
交于点
.
的值;
(2)若
,求多面体
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a3fd5284e160896f07ce367645fd04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a09d03d26008b17d89e98125eff110c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/747e7c4b2f940a9f0a7300a5d0f11cdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d3c24c0a11fa3e09841f884ba666043.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/079939b57b622b28d3ac3d1b9705eaef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3af39a146d2014f46f9972c1723da3e8.png)
您最近一年使用:0次
解题方法
8 . 如图所示,正方体
的棱长为
,
、
、
分别为
、
、
的中点,则下列说法正确的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/26/4dd40306-533e-4088-89e5-4865b61ed853.png?resizew=154)
A.直线![]() ![]() |
B.直线![]() ![]() |
C.平面![]() ![]() |
D.点![]() ![]() ![]() |
您最近一年使用:0次
9 . 如图,棱长为
的正方体
中,点
,
分别是棱
,
的中点,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/7f5b15b4-e174-4f89-b4a3-778a169cc0c0.png?resizew=163)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](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/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/7f5b15b4-e174-4f89-b4a3-778a169cc0c0.png?resizew=163)
A.直线![]() ![]() |
B.![]() |
C.过![]() ![]() ![]() ![]() |
D.三棱锥![]() ![]() |
您最近一年使用:0次
解题方法
10 . 如图,三棱台
中,
,
, D为线段AC上靠近C的三等分点
(1)在线段BC上求一点E,使
平面
,并求
的值:
(2)若
,
,点
到平面ABC的距离为
,且点
在底面ABC的射影落在
内部,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0d025c1c91b88c7d9154a191b3c5c6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/3ca5c03f-e5f2-412f-a577-a385025d0ee1.png?resizew=150)
(1)在线段BC上求一点E,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/896e293411e2fd0da215ff20781cb36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb5a463a03c549b0dba6d90e7f16a2af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af614752bd8c370f34199c8635893496.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4339a40ae9d1947ec3a4b3e2fa3a16cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5a70ead34914a6ca8fb84b52dee3136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
您最近一年使用:0次