1 . 如图,在梯形
中,
,将
沿直线
翻折至
的位置,
,当三棱锥
的体积最大时,过点
的平面截三棱锥
的外接球所得的截面面积的最小值是_______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79380475955a6f7aaf925ac45bc38428.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc3322a2ad9a95bdc9fc576a7a158d4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fe9bffd0b4cd1fb8fae50db70dcaffc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f836f086a22a72e3fbe809dae934f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ecc884f5b4dc9622e90e1303bc481f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ecc884f5b4dc9622e90e1303bc481f5.png)
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解题方法
2 . 如图,正方形
和矩形
所在的平面互相垂直,点
在正方形
及其内部运动,点
在矩形
及其内部运动.设
,
,若
,当四面体
体积最大时,则该四面体的内切球半径为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dde327febef2331a4766a79b433cc02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27ba952c1209a61b00cc62aacb367292.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f138877b595987abf3397aab8f9895e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3019bf62527f7e614c49b803d7b59d8.png)
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3 . 在长方形
中,
,点E在线段AB上,
,沿
将
折起,使得
,此时四棱锥
的体积为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de745f4a313e835454881b20c7fabeb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1364213f546b37f8764ddcb59e36ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a25c28359f8d8da9eaf4672a6cf8ae4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c05986ad5fa244bc1aedf7b5d216544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5164a3cc47e266446d49127e2ef10c37.png)
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2024-05-27更新
|
326次组卷
|
2卷引用:江西省部分学校2024届高三5月大联考数学试卷
名校
解题方法
4 . 如图,在正方体
中,
分别是线段
、BD上的点.给出下列两个说法:①存在点
,对任意点
,均有
;②若
,则直线
与
恒为异面直线,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d961cdda10c3f76c8f52ff1aa10aa45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d7b64a0de3cbdfe5d348041d27e1179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
A.①、②都正确 | B.①、②都错误 | C.①正确,②错误 | D.①错误,②正确 |
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5 . 已知正四棱锥
的所有棱长都为2,点
在侧棱SC上且
,过点
且垂直于SC的平面截该棱锥,得到截面多边形
,则
的边数为__________ ,
的面积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94a45731695b5b3a1b0ff45dac9b210e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
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6 . 在通用技术课上,老师给同学们提供了一个如图所示的木质四棱锥模型
,
为正三角形,
,
,
为线段
的中点.
平面
;
(2)过点
的平面
交
于点
,沿平面
将木质四棱锥模型切割成两部分,在实施过程中为了方便切割,请你完成以下两件事情:
①在木料表面应该怎样画线?(在答题卡的图上画线要保留辅助线,并写出作图步骤);
②在木质四棱锥模型中确定
点的位置,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ad8d16722f5b9e7fd2602f14d5ffbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b0382c28547d3834ca71f3f0677695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0457394ce4f2dc8d940c565c94dcf557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500df0e782bb081e608f4bc1d576afcf.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d94061dfdcef084c7594522ae9e512a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
①在木料表面应该怎样画线?(在答题卡的图上画线要保留辅助线,并写出作图步骤);
②在木质四棱锥模型中确定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8136c029f4b31e25c56c70a1432cbe1a.png)
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7 . 阿基米德多面体是由边数不全相同的正多边形为面围成的多面体,截角四面体是阿基米德多面体其中的一种.如图所示,将棱长为3a的正四面体沿棱的三等分点作平行于底面的截面得到所有棱长均为a的截角四面体,则下列说法中正确的是( )
A.点E到平面ABC的距离为![]() |
B.直线DE与平面ABC所成角的正切值为2 |
C.该截角四面体的表面积为![]() |
D.该截角四面体存在内切球 |
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8 . 已知正三棱锥
的三条侧棱长均为
为侧棱
的中点,
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba964c27f118895f13672321aebe5f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b4424cb0af429b92e1fc168c4c70de4.png)
A.平面![]() ![]() ![]() |
B.三棱锥![]() ![]() |
C.三棱锥![]() ![]() ![]() |
D.直径为![]() |
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解题方法
9 . 如图,在棱长为
的正四面体
中,点
,
分别为
和
的重心,
为线段
上一点.则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.![]() |
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解题方法
10 . 已知球O的半径为4,平面
,
与球面分别相交,得圆C与圆D,AB为圆C与圆D的公共弦,若
,
,则点O到直线AB的距离为______ ,四面体ABCD的体积为______ .
![](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/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e315d525af44daca685149d7d1a51e.png)
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