名校
1 . 如图,已知
为等腰梯形,点
为以
为直径的半圆弧的上一点,平面
平面
为
的中点,
.
平面
;
(2)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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f8c87296e82b6db415284e4eff4e72a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f342bf87e3006d59660261cbaf5d2524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba8f7af0e091e082100c3cd7f8c487f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/422210c777ac0d625bbd81cc7601bf9b.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,四棱锥
中,底面
是边长为
的正方形,
是
的中心,
底面
,
是
的中点.
(1)求证:
平面
;
(2)若
,求三棱锥
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/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e126c16032892966489053f44b9048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/21/888665b4-0c89-485a-99d8-2534ffce9190.png?resizew=182)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/954c584f9c868d235e0fc1debb14428d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07445aa3909818a3ef93bb01182f545f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42020cfacd62b300cad053981bab9e0b.png)
您最近一年使用:0次
2023-08-20更新
|
1400次组卷
|
6卷引用:广东省惠州市惠东县惠东荣超中学2023-2024学年高二上学期开学考试数学试题
3 . 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
|
905次组卷
|
4卷引用: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
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(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】
解题方法
4 . 如图,四棱锥S-ABCD中,SD⊥AD,SD⊥CD,E,F分别是SC,SA的中点,O是底面正方形ABCD的中心,AB=SD=4.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/4/5e6b82da-68dc-4cf8-8ff2-28463ce81e20.png?resizew=186)
(1)求证:EO
平面SAD;
(2)求异面直线EO与BF所成角的余弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/4/5e6b82da-68dc-4cf8-8ff2-28463ce81e20.png?resizew=186)
(1)求证:EO
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
(2)求异面直线EO与BF所成角的余弦值.
您最近一年使用:0次
5 . 如图,四棱锥
的底面是边长为2的菱形,
,对角线AC与BD相交于点O,
平面ABCD,PB与底面ABCD所成角为
,点E是PB的中点.
(1)证明:
平面PAD;
(2)求点E到平面PAD的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fccaf36651e0ac62b3ccf9edd74372a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84ad334c6d980f01aaa3bf6be547a7fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ad1b0a76a887783392268ae203ad22.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/1/9ff50cd1-5ffe-469c-beaf-fbb9b49f54d3.png?resizew=164)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4610344fed3177e36cdf9cdf11e81e4.png)
(2)求点E到平面PAD的距离.
您最近一年使用:0次
名校
6 . 如图,在四棱锥
中,四边形
是矩形,
是正三角形,且平面
平面
,
,
为棱
的中点,
.
为棱
的中点,求证:
平面
;
(2)若
为棱
上一点,且
,求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5830322dd2824ed012a68f1a2bd9c742.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877582b5387278008d14fe5932622fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28f79db7c270b6ff9fb0a538ee201cfe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c77e9c89b7275b0c1a9af5c9a72e5968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/375b7f0808edd827ef15b0eb2ca0862a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b81fb655624ff75a5eab94de9b8c8e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d923a338dd2d2e29336b42574d38448.png)
您最近一年使用:0次
2023-11-05更新
|
794次组卷
|
2卷引用:广东省惠州市惠东县2024届高三上学期第二次教学质量检测数学试题
名校
7 . 在正方体
中,设
,
分别为棱
,
的中点.
(1)证明:
平面
;
(2)求二面角
的余弦值.
![](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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/31/fc6f5cea-c0a1-4843-b639-057813855140.png?resizew=169)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0684e0b09b04661c602437982c0397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7513c5dc6e1d35f76020f8f60c95669.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4408bbbd7d295e7b3900e53d70f28543.png)
您最近一年使用:0次
2023-10-13更新
|
496次组卷
|
6卷引用:广东省惠州市龙门县高级中学2023-2024学年高二上学期期中数学试题
广东省惠州市龙门县高级中学2023-2024学年高二上学期期中数学试题江苏省连云港市2023-2024学年高三上学期教学质量调研(一)数学试题(已下线)江苏省南通市如皋市2023-2024学年高三上学期教学质量调研(一)数学试题江苏省淮安市马坝高级中学2023-2024学年高三上学期10月学情调研测试数学试题重庆市九龙坡区杨家坪中学2023-2024学年高二上学期第二次月考数学试题(已下线)专题09 立体几何(5大易错点分析+解题模板+举一反三+易错题通关)-2
解题方法
8 . 如图,在正方体
中,E为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/30/df0db5fa-34e5-4640-b77c-3ad402c30236.png?resizew=164)
(1)求证:
平面
;
(2)求点D到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/30/df0db5fa-34e5-4640-b77c-3ad402c30236.png?resizew=164)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5830646a912c3a916beac4f88c116b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
(2)求点D到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
您最近一年使用:0次
2023-10-11更新
|
130次组卷
|
2卷引用:广东省惠州市龙门县高级中学2023-2024学年高二上学期期中数学试题
名校
解题方法
9 . 如图,在正方体
中,
是棱
的中点.
(1)试判断直线
与平面
的位置关系,并说明理由;
(2)若正方体
的棱长为2,求点
到平面
的距离.
![](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/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/10/166d3242-22f6-4106-906a-c2002d322d52.png?resizew=168)
(1)试判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(2)若正方体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211ad5a06b505b8365a62c1946f3cb7.png)
您最近一年使用:0次
2023-07-08更新
|
533次组卷
|
2卷引用:广东省惠州市2022-2023学年高一下学期期末数学试题
10 . 在直三棱柱
中,
,
,
,点
在棱
上,
,
是
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0deedd57bb687af456b19bd22d20ffcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1364213f546b37f8764ddcb59e36ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
A.三棱柱![]() ![]() |
B.三棱柱![]() ![]() |
C.![]() ![]() |
D.![]() ![]() |
您最近一年使用:0次
2023-07-08更新
|
329次组卷
|
5卷引用:广东省惠州市惠东县惠东荣超中学2023-2024学年高二上学期开学考试数学试题