1 . 在长方体
中,
,
为
的中点,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/552a7180130060ccda3555cb96fce6d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657dffbd3623b705f871878fbd9df57e.png)
![](https://img.xkw.com/dksih/QBM/2021/10/26/2837800444248064/2838556561825792/STEM/af39ceebf9d04887aa11a9046ca189e3.png?resizew=235)
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2 . 直三棱柱
中,已知
,
,
.
![](https://img.xkw.com/dksih/QBM/2022/6/10/2998364128813056/3042847401287680/STEM/971ddff8bf49412ea48281211885eec8.png?resizew=356)
(1)若M为
的中点,求三棱锥
的体积
(2)将两块形状与该直三棱柱完全相同的木料按如下图所示两种方案沿阴影面进行切割,把木料一分为二,留下体积较大的一块木料.根据你所学的知识,请判断采用哪一种方案会使留下的木料表面积较大,并求出这个较大的表面积和说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883fc5e3faf39829d60804b59deb1730.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d6baf49925a5bcb359b542d45067c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://img.xkw.com/dksih/QBM/2022/6/10/2998364128813056/3042847401287680/STEM/971ddff8bf49412ea48281211885eec8.png?resizew=356)
(1)若M为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0a7b3edad9191d5489bb9c28ff92ce5.png)
(2)将两块形状与该直三棱柱完全相同的木料按如下图所示两种方案沿阴影面进行切割,把木料一分为二,留下体积较大的一块木料.根据你所学的知识,请判断采用哪一种方案会使留下的木料表面积较大,并求出这个较大的表面积和说明理由.
您最近一年使用:0次
3 . 如图,四棱锥E﹣ABCD中,底面ABCD为菱形,BE⊥平面ABCD.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/3b1d077d-76e0-4055-a439-627b2cc88d1c.png?resizew=231)
(1)求证:AC⊥平面BED;
(2)若∠ABC=120°,AE⊥EC,AB=2,求三棱锥E﹣ABD的体积.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/3b1d077d-76e0-4055-a439-627b2cc88d1c.png?resizew=231)
(1)求证:AC⊥平面BED;
(2)若∠ABC=120°,AE⊥EC,AB=2,求三棱锥E﹣ABD的体积.
您最近一年使用:0次
11-12高一上·广东东莞·期末
解题方法
4 . 如图,正方形
的边长为1,正方形
所在平面与平面
互相垂直,
是
的中点.
(1)求证:
平面
;
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570005425086464/1570005430362112/STEM/d6c5a08cbae746979405ee12c3f845d3.png)
(2)求证:
;
(3)求三棱锥
的体积.
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570005425086464/1570005430362112/STEM/90cd07ee6933459d874efbbf13591d41.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570005425086464/1570005430362112/STEM/e6b6b9bdc79d4f94927976d669a4d5b0.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570005425086464/1570005430362112/STEM/90cd07ee6933459d874efbbf13591d41.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570005425086464/1570005430362112/STEM/250059b13f2440eeb25da7eed33a2236.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570005425086464/1570005430362112/STEM/6c6f24b8ed1b4980be4017bdda08d3b0.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570005425086464/1570005430362112/STEM/9fe00274328b462192303570b05359cb.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570005425086464/1570005430362112/STEM/da0cee6af4ab4ea49d5f1d02e1465167.png)
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570005425086464/1570005430362112/STEM/d6c5a08cbae746979405ee12c3f845d3.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c7274d4381e1cdd7483a543b1fde7c.png)
(3)求三棱锥
![](https://img.xkw.com/dksih/QBM/2011/2/22/1570005425086464/1570005430362112/STEM/eeb23cc551664abf8b835a0649a95f12.png)
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5 . 一个几何体的三视图如图所示,其俯视图为正三角形,则这个几何体的体积为
![](https://img.xkw.com/dksih/QBM/2014/4/25/1571662821244928/1571662826291200/STEM/8da4ee3950824b1d80d546003e2fbb94.png)
![](https://img.xkw.com/dksih/QBM/2014/4/25/1571662821244928/1571662826291200/STEM/8da4ee3950824b1d80d546003e2fbb94.png)
A.12![]() | B.36![]() | C.27![]() | D.6 |
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6 . 《九章算术》中记载了公元前344年商鞅督造的一种标准量器——商鞅同方升,其主体部分的三视图如图所示,则该量器的容积为
![](https://img.xkw.com/dksih/QBM/2017/4/28/1675359355437056/1679921867612160/STEM/dbb080c38a9d467e80fbe7eca8fea611.png?resizew=417)
![](https://img.xkw.com/dksih/QBM/2017/4/28/1675359355437056/1679921867612160/STEM/dbb080c38a9d467e80fbe7eca8fea611.png?resizew=417)
A.252 | B.189 | C.126 | D.63 |
您最近一年使用:0次
2017-05-03更新
|
269次组卷
|
2卷引用:广东省东莞市2017届高三第二次模拟测试数学理试题
7 . 已知正四棱台的上下底边长分别为
,正四棱台体积为
,则此表面积为______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e8f2f2bcb8c77fb20b9d4f9f53255e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd442b32f40fe61def96c2fca0ad37f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88ce13774b09ff2edddaf21a072cf60a.png)
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