1 . 如图,在四面体
中,
,
,
两两垂直,已知
,
,则点O到平面
的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50bf7d7fa347c09dedde116bb787a3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98c78f77e5b86ccd537e5f027de9ffe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
2 . 随着北京中轴线申遗工作的进行,古建筑备受关注.故宫不仅是世界上现存规模最大、保存最为完整的木质结构古建筑之一,更是北京中轴线的“中心”.图1是古建筑之首的太和殿,它的重檐庑(wŭ)殿顶可近似看作图2所示的几何体,其中底面
是矩形,
,四边形
是两个全等的等腰梯形,
是两个全等的等腰三角形.若
,则该几何体的体积为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/24/95188fe8-732e-4284-9b64-2d3d714d1100.png?resizew=355)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99c17bb8b8e4542af2f7be4fb92f677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/518c52e86814e825a2f8540375cc198b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/936208a930533ebec1f94b009d94fb7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8ff480799eef2540c0f5002314bb2f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/24/95188fe8-732e-4284-9b64-2d3d714d1100.png?resizew=355)
A.720 | B.![]() | C.![]() | D.1080 |
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3 . 已知二面角
,点
与棱l的距离为
,与半平面
所在平面的距离为3.
(1)求二面角
的余弦值;
(2)设
,动点
在半平面
所在平面上,满足
.
(i)求Q运动轨迹的长度;
(ii)求四面体
体积的最大可能值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85fde9a77ea526c57835071467fd3da5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50690dab38f4512eb72e18b7f86cf6f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aec748163f49d0331620c5bb70d1404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b7ddeaf0a0ed481573cb15a7c79a6d.png)
(i)求Q运动轨迹的长度;
(ii)求四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d4ae321214d53714751d7c52aba8f45.png)
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解题方法
4 . 如图,
平面
,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/23/e15ed5cd-9e07-4c57-9884-129b7fb64b7a.png?resizew=155)
(1)求证:
平面
;
(2)求平面
与平面
夹角的余弦值;
(3)若点E到平面
的距离为
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b4b0e9ba8c5913398f3260c3a50ba6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d262480ffb55b7617f44b63f130c154a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88dac2c17c765517c2163ab43bbe1038.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/23/e15ed5cd-9e07-4c57-9884-129b7fb64b7a.png?resizew=155)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d32e76582bf550593fdef53e081225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65277734669566578cbb7d690bb200fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dfaad4c4467e27421876d8f2a4371d2.png)
(3)若点E到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7116071164cdc45f5d312a437c68bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f7b603a64608e5b76215af4d3905c55.png)
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5 . 如图,在正方体
中,E为棱
的中点.动点P沿着棱
从点D向点C移动,对于下列三个结论:
①存在点P,使得
;
②
的面积越来越小;
③四面体
的体积不变.
其中,所有正确结论的个数是( ).
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/e05efe2d-0405-448d-b1e8-099399b0c636.png?resizew=165)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
①存在点P,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/656aceec19543470bd58ed3d304d155d.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c1b7f8c6e4793af4336d02addfbfbb.png)
③四面体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6738d05f0c7e4f0076fd5c094a4fb51c.png)
其中,所有正确结论的个数是( ).
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/17/e05efe2d-0405-448d-b1e8-099399b0c636.png?resizew=165)
A.0 | B.1 | C.2 | D.3 |
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2023-12-17更新
|
217次组卷
|
2卷引用:北京市海淀区北京理工大附中高三上学期12月练习数学试题
名校
解题方法
6 . 已知直三棱柱
,则三棱柱
的体积的最大值为__________ ;此时棱柱的高为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dca372da7838265832b761428775bfd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
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2023-12-05更新
|
899次组卷
|
3卷引用:北京市海淀区北京交大附中2024届高三上学期12月诊断练习数学试题
名校
7 . 如图,在棱长为1的正方体
中,
是棱
上的一个动点,给出下列四个结论:
①三棱锥
的体积为定值;
②存在点
使得
平面
;
③
的最小值为
;
④对每一个点
,在棱
上总存在一点
,使得
平面
;
⑤
是线段
上的一个动点,过点
的截面
垂直于
,则截面
的面积的最小值为
.
其中正确的命题的序号是________ .
![](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/2777840758e70e7dbbc18cef8f3d6d2b.png)
①三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8bcd4d16a1f2e89bb43fd1731a05ab1.png)
②存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/565133e91e3ace2b2187cfc6f1db5be6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a83c0b8db2205a6815811aa4ff5390f.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5a2fee2a78208f17068351405599b0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1f190b17530d81d927c358ac84757a4.png)
④对每一个点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80aa75fd1351786abd39fa546f3c7833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a83c0b8db2205a6815811aa4ff5390f.png)
⑤
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15a424b50eaeafa6f302ffd95476cb86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839c7616cd0d90265f4b2c9c021254fe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/5/68789707-893b-4b2a-b900-6f451484d747.png?resizew=165)
其中正确的命题的序号是
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8 . 某钟楼的钟面部分是一个正方体,在该正方体的四个侧面分别有四个时钟,如果四个时钟都是准确的,那么从零点开始到十二点的过程中,相邻两个面上的时针所成的角为
的位置有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
A.1个 | B.2个 | C.3个 | D.4个 |
您最近一年使用:0次
2023-11-15更新
|
156次组卷
|
2卷引用:北京市东城区景山学校2024届高三上学期12月月考数学试题
名校
解题方法
9 . 如图,棱长为2的正方体
中,E、F分别为棱
的中点,G为面对角线
上一个动点,则下列选项中正确的是 _____ .
①三棱锥
的体积为定值
.
②存在
线段
,使平面
平面
.
③G为
上靠近
的四等分点时,直线
与
所成角最小.
④若平面
与棱
有交点,记交点分别为M,N,则
的取值范围是
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60e3e67d56b946fd77a7f9d12222e0a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
①三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79d516856d92c60553659a22a45118e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
②存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd1762bd4dae0766e3bcb49c29a57a00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1fd975b889bfe7ddcec0de56b6f23ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf9628142422a4884bd59538da6d312.png)
③G为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
④若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe8a84ca3a13f82aff1a022edc66065.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374fe9986ebbc986fc422e514ab93a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11dbfa1097bc37f9c0072bcb7daeb2d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b88477451cc7efc1cacf4b03e4b13d3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/23/f665888a-2601-41c9-80e0-6fd31aabbd12.png?resizew=174)
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10 . 在正方体
中,
为棱
上的动点,
为线段
的中点.给出下列四个结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/11/728f8e20-d71a-4a9d-af5a-2f992985d287.png?resizew=160)
①
;
②直线
与平面
的夹角不变;
③三棱锥
的体积不变;
④点
到
,
,
,
四点的距离相等.
其中,所有正确结论的序号为_____________________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9601d29de0a884953b039ee72f0158fe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/11/728f8e20-d71a-4a9d-af5a-2f992985d287.png?resizew=160)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3681ff426cdbe7184eeb004ff0eaefb.png)
②直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/557f8ff92d79a9d464ff13de17f3eae7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdcfe69b939fd1c271747fe9d37ccdf9.png)
③三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccc3bf74119692ac98eb24fcfa2a3f9f.png)
④点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
其中,所有正确结论的序号为
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