1 . 已知一个表面积为
的球与正三棱柱的各个面都相切,则此正三棱柱的体积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c96c94a6a97b34d8ccc793d3be02aff.png)
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2 . 已知从点
发出的光线经
轴反射,反射光线与圆
相切,其反射光线的斜率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c3316c2f17c0b3a99cc520b6aaa711.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a8a746db0901d810caffa54ae3f29f.png)
A.![]() | B.2 | C.![]() | D.![]() ![]() |
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3 . 若正四面体
的棱长为
,M为棱
上的动点,则当三棱锥
的外接球的体积最小时,三棱锥
的体积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d90f940f5693b22ddf2e7c761887d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d90f940f5693b22ddf2e7c761887d8.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5卷引用:重庆市乌江新高考协作体2024届高考模拟监测(二)数学试题
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4 . 已知平面向量
均为单位向量,且
,若
,则
的取值范围为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c87f0ca6032f85abf58764ccaafd40bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5af70c2a213ed4632100dc5c3fb07bde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83634e314df24df73ae37d25a44d20e3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5 . 如图,边长为2的正方形
中,
分别是
的中点,将
分别沿
折起,使
重合于点
,则三棱锥
的外接球的体积为__________ ;设直线
与平面
所成角分别为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0890d955d54daafbaf9e9662ea23ecb.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374fe9986ebbc986fc422e514ab93a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d0a181fb3a5a51245c82f94eebadcab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0e1b35ce4e9edff774c986d78e4b39f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16fd1bc6147d69777b26a35d48522f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0368bbedfea716e7af7919d7d4ca842a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61ba63ad02b1d5af2982fac3d91eb15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0890d955d54daafbaf9e9662ea23ecb.png)
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6 . 如图,已知在正三棱柱
中,
为边
的中点.
;
(2)求三棱锥
的体积;
(3)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e0bb803cd8c9c8d598416c2816aef6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa8345302e8036af33d4598282144d7.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa58d518fe175f71265a2e405f1d253.png)
(3)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78ceb31247add8ca7b0853e801e1d125.png)
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7 . 如图,已知四边形
是平行四边形,
分别是
的中点,点P在平面
内的射影为
与平面
所成角的正切值为2,则直线
与
所成角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1457d2e76a5b86de1abf121c51eb9d35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b0a09ed9c929979697fa393e01940aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 已知三棱锥
的四个顶点均在球O上,
平面
为等腰直角三角形,A为直角顶点.若
,且
,则球O的表面积为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1258223a94b8d5790053de9c640db8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0470bb4b86ddf002cc5b146c2abe47a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced1596b1848adb52de3d0943b9fc5f2.png)
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9 . 已知三棱锥
,
为
中点,
,
,且
,
,
,
,则三棱锥
外接球的表面积为______ ,过点
的平面截该三棱锥外接球所得截面面积的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d9ef979b9f27a28cbda6923e888ccc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d900531973c546625694146fa1509ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd3eb538f36e6e722e4ce125266b99b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca036d049f5205cf04cb1b9c5cd03f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3755b2bcf7516eedb26a27ad73657216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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10 . 已知四面体ABCD中,
,若四面体ABCD的外接球的表面积为7
,则四面体ABCD的体积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59102f6a07322ec488d98289131f0792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
A.1 | B.2 | C.![]() | D.![]() |
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