名校
解题方法
1 . 已知两个正四棱锥
与
均内接于球
,满足
和
,则球
的体积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55c6caa0455442437177ab9b995df37b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50488f7443c0b740ed0b645c519e4e46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6834ac70927ae08d7d36a1922403c9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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2 . 如图,在三棱柱
中,正方形
的棱长为2,
,点M为AB中点,
.
为直三棱柱;
(2)求直线
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c645d1dea7ca8a6eb931635dcf63d6f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4149c3692068ea18563a4ef56d9d1cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ef601ca1f9c4c031adab4ffed297f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e363082228a653eb5b0dbc3c6161a9c9.png)
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3 . 如图所示,点
为正方体形木料
上底面的动点,则下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
A.三棱锥![]() |
B.存在点![]() ![]() ![]() |
C.不存在点![]() ![]() ![]() |
D.经过点![]() ![]() ![]() ![]() ![]() ![]() |
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解题方法
4 . 如图所示,在四棱锥
中,底面ABCD是边长为2的正方形,
平面ABCD,
,则下列选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41cd5c4f8b106d01e0e431078e1a468b.png)
A.该四棱锥的外接球表面积为![]() |
B.若动点Q在三角形![]() ![]() ![]() |
C.若点E为PA的中点,则![]() |
D.若动点Q在正方形ABCD内(含边界),且![]() ![]() ![]() |
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解题方法
5 . 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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3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
6 . 已知
是空间中两条不同的直线,
,
是两个不同的平面,则下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
A.若![]() ![]() ![]() | B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() | D.若![]() ![]() ![]() |
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4卷引用:江西省宜春市第一中学2024届高三下学期第三次模拟考试数学试卷
江西省宜春市第一中学2024届高三下学期第三次模拟考试数学试卷(已下线)6.5.1 直线与平面垂直-同步精品课堂(北师大版2019必修第二册)山东省德州市夏津育中万隆中英文高级中学2023-2024学年高一下学期5月月考数学试题(已下线)专题07 立体几何初步(1)-期末考点大串讲(人教B版2019必修第四册)
名校
解题方法
7 . 如图,在四棱锥
中,
平面
,
,
,
,
,
,
分别为
,
的中点.
的体积;
(2)求直线
与平面
所成线面角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.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/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/487530f6d17b94493d03b004aa3462d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3e27f6e6d1592408508cc9fd14d480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4795ee1f96b430529934e2231b38885d.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/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fc203fe37519a2fef5ed3f7f2e46d94.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/149596fee6ed1e2d19fd8dadc14a8baf.png)
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2卷引用:黑龙江省哈尔滨市第九中学校2024届高三第四次模拟考试数学试卷.
名校
解题方法
8 . 已知四棱锥
的底面是边长为3的正方形,
平面
为等腰三角形,
为棱
上靠近
的三等分点,点
在棱
上运动,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fb2e071d4e01107dcf7d95cbb86b415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28efccebdbe5d05f441624633478b44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defa5b53043ae802bb1af7d14374406d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
A.![]() ![]() |
B.![]() |
C.![]() |
D.点![]() ![]() ![]() |
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解题方法
9 . 如图,在棱长为
的正方体
中,点
在线段
上运动,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
A.平面![]() ![]() |
B.三棱锥![]() |
C.异面直线![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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10 . 如图,在棱长为1的正方体
中,M为平面ABCD内一动点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
A.若M在线段AB上,则![]() ![]() |
B.平面![]() ![]() |
C.若![]() ![]() |
D.对于给定的点M,过M有且仅有3条直线与直线![]() ![]() ![]() |
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