1 . 我国古代数学名著《九章算术》中,将底面为直角三角形且侧棱垂直于底面的三棱柱称之为堑堵;将底面为矩形且一侧棱垂直于底面的四棱锥称之为阳马;将四个面均为直角三角形的四面体称之为鳖臑[biē nào].某学校科学小组为了节约材料,拟依托校园内垂直的两面墙和地面搭建一个堑堵形的封闭的实验室
,
是边长为2的正方形.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/45fde4d8-c125-4b27-aef1-9044ed46e1e8.png?resizew=377)
(1)若
是等腰三角形,在图2的网格中(每个小方格都是边长为1的正方形)画出堑堵的三视图;
(2)若
,
在
上,证明:
,并回答四面体
是否为鳖臑,若是,写出其每个面的直角(只需写出结论);若不是,请说明理由;
(3)当阳马
的体积最大时,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b7b7793d29d66dfdd89e7a6564a35c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/20/45fde4d8-c125-4b27-aef1-9044ed46e1e8.png?resizew=377)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a543df08305d4a848a980969bb002a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bdcec400a6a9311072505df48fb0fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22725912baecf50924d950b915d0156.png)
(3)当阳马
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb1b9bf22bd3ca350a2651a7550e8ba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
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4卷引用:上海市闵行区2018-2019学年高二下学期期末数学试题
上海市闵行区2018-2019学年高二下学期期末数学试题(已下线)专题4.5 简单几何体【压轴题型专项训练】-2020-2021学年高二数学下学期期末专项复习(沪教版)江苏省南通市如皋中学2020-2021学年高一下学期5月月考数学试题(已下线)第06讲 点面、线面、面面、异面直线的距离(核心考点讲与练)-2022-2023学年高二数学考试满分全攻略(沪教版2020必修第三册)
名校
2 . 如图为某一几何体的展开图,其中
是边长为
的正方形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a21f3055411b6927d08f328da969b017.png)
,点
及
共线.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/d1687fa9-e9d9-4985-84e6-39585e4167dd.png?resizew=165)
(1)沿图中虚线将它们折叠起来,使
四点重合,请画出其直观图,试问需要几个这样的几何体才能拼成一个棱长为
的正方体
?
(2)设正方体
的棱
的中点为
,求平面
与平面
所成二面角(锐角)的余弦值.
(3)在正方体
的
边上是否存在一点
,使得
点到平面
的距离为
,若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a21f3055411b6927d08f328da969b017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0437348e1bf7c037e7e4904609b9ba2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec835ef17014181e96cfb481dc72ecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60e2cbbf7a93719b3196a7d931ef638f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/11/d1687fa9-e9d9-4985-84e6-39585e4167dd.png?resizew=165)
(1)沿图中虚线将它们折叠起来,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4457a029cd930f0052f1c80cfe06d00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
(2)设正方体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69bcb3226e013650b7d8827c31dd41d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(3)在正方体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5105eb24aa12b2163d9c7f50ec1ef2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
您最近一年使用:0次
2019-12-11更新
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4卷引用:上海市上海师大附中2017-2018学年高二下学期期末数学试题
上海市上海师大附中2017-2018学年高二下学期期末数学试题(已下线)专题4.4 空间直线与平面【压轴题型专项训练】-2020-2021学年高二数学下学期期末专项复习(沪教版)上海市向明中学2023-2024学年高二上学期10月月考数学试题上海市闵行区六校2023-2024学年高二上学期期中联考数学试题