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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2024-03-27更新
|
870次组卷
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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 . 已知直线l:
,点
、
,设
,
,下列条件中可以推出直线l与线段AB的延长线相交的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50f6e1f67dc15c3cf135a78af95c70fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fea52382139e3bf9d91ea7ef28ea914a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c32636ce17db5e0110a65d3cdcf9aa0f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 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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解题方法
4 . 已知平行四边形
的三条边所在直线的方程分别是
,
的交点为
的交点为
,且平行四边形
的面积为5,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/197c681b07a2db592cbb1366cbbcd833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9be502fa855f0617f1ba00f51462d5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69273f483e3ad012b1ca190314b04605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.![]() ![]() |
B.![]() ![]() |
C.平行四边形![]() ![]() |
D.平行四边形![]() ![]() |
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解题方法
5 . 圆锥甲、乙、丙的母线与底面所成的角相等,设甲、乙、丙的体积分别为
,侧面积分别为
,高分别为
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06e1fa43badbcca84eb7310e1e039335.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcf4e20ea341827ce5f9552daee39462.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f30c6b35e54148320970c2376339764.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa120a7758ba5e47480629c71a24088d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d023116866b910ec5eeb9de97c542f9.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
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6 . 柳编技艺在我国已有上千年的历史,如今柳编产品已经入选国家非物质文化遗产名录.如图所示;这是用柳条编织的圆台形米斗,上底直径
,下底直径
,高为
,则该米斗的容积大概为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/3/d6022429-e4cc-4142-89fc-c28365f2d1cb.png?resizew=129)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3668a3f3ce5b8a272ad92c2ebd233f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe9f7abf7bcf4e1aa2579cd191d7761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3668a3f3ce5b8a272ad92c2ebd233f5a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/3/d6022429-e4cc-4142-89fc-c28365f2d1cb.png?resizew=129)
A.9升 | B.15升 | C.19升 | D.21升 |
您最近一年使用:0次
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解题方法
7 . 陀螺是中国传统民俗体育游戏,流传甚广,打陀螺已被列入第五批国家级非物质文化遗产代表性项目名录.陀螺结构分为上下两部分:上部分为木质件,下部分为球形钢珠.其中木质件的形状为上部是底面半径为
,高为
的圆柱,下部为上底半径为
,下底半径为
,高为
的圆台.若陀螺的木质件由一个球形原料经车床一次性车制而成,那么原料的半径最小为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/4/3439458f-8b2b-4872-a4df-64dde97ca759.png?resizew=78)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0f4b6bd1da1d5d64b08f4b0f2243033.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db0eccafad38c29dce15c29fa6ad45c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0f4b6bd1da1d5d64b08f4b0f2243033.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcca994b2d01857bb0f6e34b0dad20b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36ad674c4d1a42c1c6a633281ed29b88.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/4/3439458f-8b2b-4872-a4df-64dde97ca759.png?resizew=78)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-03-04更新
|
399次组卷
|
3卷引用:河北省2024届高三下学期大数据应用调研联合测评(V)数学试题
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解题方法
8 . 现准备给一半径为
的实心球体玩具制作一个圆台型带盖的纸质包装盒,要使制成的包装盒能装下该球体玩具,且该包装盒的下底面是半径为
的圆,则制成的包装盒的容积最小为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd6f4250ca6b1b9bce234a01f00d44d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/095ab4a92bf822e175d370e6d0c8a730.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/3/01cbcbe2-203d-403e-bf58-0aedae50cda3.png?resizew=162)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-03-04更新
|
601次组卷
|
3卷引用:湖南省三湘创新发展联合体2023-2024学年高三下学期2月开学统试数学试题
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9 . 已知圆
经过点
,且点
到点
的距离为3,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/945066b2767be49535b0f9529649b834.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/111dc13e1517105f7b1841792f72664d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bec550c01b4f075f22ab67f5e55ed5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/451fc6e4248b63e70595f23842f06c93.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
10 . 在平面直角坐标系中,过直线
上任一点
作该直线的垂线
,
,线段
的中垂线与直线
交于点
.
(1)当
在直线
上运动时,求点
的轨迹
的方程;
(2)过
向圆
引两条切线,与轨迹
的另一个交点分别为
,
.
(i)证明:直线
与圆
也相切;
(ii)求
周长的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/236a066876764d090523afe0ea734a21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50154acc6ad77c6c777fffe3a08afb59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2273ae1ee99cec9c1304323bc9ebf75f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f817fa2d2a8c4e38191900ed7730c879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(i)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(ii)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
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