1 . 一个三棱锥形木料
,其中
是边长为
的等边三角形,
底面
,二面角
的大小为
,则点A到平面PBC的距离为__________
.若将木料削成以A为顶点的圆锥,且圆锥的底面在侧面PBC内,则圆锥体积的最大值为_________
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ff7bcb98a21e7c3da0e9367db50d1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b796bbaeb8450404c2d146283562006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af089fd292ba69ddef79e9ab1cac77ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f694e6b5440ffc47cd59dc37f75e0f7.png)
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5卷引用:江苏省南通市海安高级中学2024届高三下学期开学考试数学试题
江苏省南通市海安高级中学2024届高三下学期开学考试数学试题江苏省南通市海安市2023-2024学年高三上学期期初学业质量监测数学试题河南省南阳市西峡县第一高级中学2023-2024学年高二下学期第一次调研测试数学试卷江苏省扬州市高邮市临泽中学2024届高三下学期一模模拟数学试题(已下线)第四章 立体几何解题通法 专题五 平移变换法 微点3 平移变换法综合训练【培优版】
名校
2 . 在四棱锥
中,
是矩形,
为棱
上一点,则下列结论正确的是( )
![](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/5130ddc74af23f8ccfaa5974a223e84c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d4db9b82b67efe45a02fca32bfcf5dc.png)
A.点![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.四棱锥![]() ![]() |
D.直线![]() ![]() ![]() |
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3 . 已知球
的半径为2,点
是球
表面上的定点,且
,
,点
是球
表面上的动点,满足
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f6a21e67e232d5db608299f0bc364ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64ffe9de3a135dac9e970edd2bc979b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/224dc2a6139f056e1a219acc648eae6a.png)
A.有且仅有一个点![]() ![]() | B.点![]() ![]() ![]() |
C.存在点![]() ![]() ![]() | D.![]() ![]() |
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2卷引用:河南省“顶尖计划”2023-2024学年高中毕业班上学期第一次联考数学试题
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解题方法
4 . 如图所示,已知圆柱的侧面展开图的面积为
,底面直径
,
为底面上异于
,
的点,且
求:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/8/4996629e-2d5a-40f3-97c0-c2cdec513724.png?resizew=140)
(1)二面角
的余弦值![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e1d918e7fb74176679d526cdfc8fa16.png)
(2)点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997b5842f3d4eae1989debee9ae41b9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714cc3707bba3bfdb56e251999be8592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d3ac7c2d973edf5a7faa608d168dbe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/8/4996629e-2d5a-40f3-97c0-c2cdec513724.png?resizew=140)
(1)二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca6d1c5eace748465b2dad5065f5111c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e1d918e7fb74176679d526cdfc8fa16.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4eb7e9ad5486cf1c5e506b20c5469e8.png)
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3卷引用:河北市承德市双滦区实验中学2023-2024学年高二上学期开学摸底数学试题
解题方法
5 . 如图,在等腰梯形
中,
,
,
,M为
中点,将
沿直线
翻折至
.则在
翻折过程中,下列判断正确的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80f51c31583fea58fde645474d60b8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e73c8c1d2ba6b29b301380a45dfbcdd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad09a769a75b107390b9eeccc929f761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb0a272d6917c569c36b60dd9ec8094.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad09a769a75b107390b9eeccc929f761.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/7/e14c6464-1c3e-4558-ac81-bea434f26bc2.png?resizew=186)
A.在![]() ![]() ![]() |
B.存在某个位置,使得![]() |
C.当![]() ![]() ![]() ![]() |
D.四棱锥![]() |
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2022·全国·模拟预测
名校
解题方法
6 . 已知圆锥PO的轴截面PAB是等腰直角三角形,
,M是圆锥侧面上一点,若点M到圆锥底面的距离为1,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
A.点M的轨迹是半径为1的圆 | B.存在点M,使得![]() |
C.三棱锥![]() ![]() | D.![]() ![]() |
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2022-12-05更新
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962次组卷
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3卷引用:浙江省名校协作体2022-2023学年高三下学期开学联考适应性考试数学试题
浙江省名校协作体2022-2023学年高三下学期开学联考适应性考试数学试题(已下线)2023年普通高等学校招生全国统一考试数学领航卷(一)江西省吉安市峡江中学2022-2023学年高二上学期期末数学试题
名校
解题方法
7 . 如图,在三棱锥
中,三条侧棱OA,OB,OC两两垂直,且
,M为
内部一动点,过M分别作平面OAB,平面OBC,平面OAC的垂线,垂足分别为P,Q,R.
![](https://img.xkw.com/dksih/QBM/2022/5/7/2974506010230784/2975624099708928/STEM/2b11d325-7f6d-4c17-85a9-065fc761d527.png?resizew=271)
①直线PR与直线BC是异面直线;
②
为定值;
③三棱锥
的外接球表面积的最小值为
;
④当
时,平面PQR与平面OBC所成的锐二面角为45°.
则以上结论中所有正确结论的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbab39da847da8a559994b6c6004aa60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://img.xkw.com/dksih/QBM/2022/5/7/2974506010230784/2975624099708928/STEM/2b11d325-7f6d-4c17-85a9-065fc761d527.png?resizew=271)
①直线PR与直线BC是异面直线;
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b4389530f4d31bc0ae46d0edfcdd2dd.png)
③三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64bab74dadb5557a3762947e52feb532.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4966e5af166b69a0a38a98abf555b6b.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38db6f3badb51bef6fa220ce110af854.png)
则以上结论中所有正确结论的序号是
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3卷引用:福建省福州第四中学2022-2023学年高二下学期开学考数学试题
8 . 正方体
中,
是的
中点,
是线段
上的一点. 给出下列命题:
![](https://img.xkw.com/dksih/QBM/2021/8/13/2785290337861632/2786879779913728/STEM/2e40dda5-15df-439c-9473-34d7e5d2bbd6.png?resizew=233)
① 平面
中一定存在直线与平面
垂直;
② 平面
中一定存在直线与平面
平行;
③ 平面
与平面
所成的锐二面角不小于
;
④ 当点
从点
移动到点E时,点
到平面
的距离逐渐减小.其中,所有真命题的序号是___________________ .
![](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/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce1b066f8869d0ff4513f7a99745125.png)
![](https://img.xkw.com/dksih/QBM/2021/8/13/2785290337861632/2786879779913728/STEM/2e40dda5-15df-439c-9473-34d7e5d2bbd6.png?resizew=233)
① 平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
② 平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
③ 平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
④ 当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68a7bf0da4f7c6f739d2e2461ad9b7.png)
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2021-08-15更新
|
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3卷引用:江西省南昌市豫章中学2021-2022学年高二入学调研(B)数学(文)试题