题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125336-99178.jpg)
(Ⅰ)求证:AC⊥平面BDEF;
(Ⅱ)求证:平面BDGH//平面AEF;
(Ⅲ)求多面体ABCDEF的体积.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125336-42856.png)
解析
试题分析:(Ⅰ)∵平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125336-86162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125336-67195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125336-50721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125337-46365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125337-45870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125337-25159.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125336-67195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125337-44646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125336-50721.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125337-46365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125337-45870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125337-11891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125337-29984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125338-64023.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125338-23268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125338-61333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125338-58564.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125338-29618.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125338-64023.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125339-91095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125338-64023.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125339-59483.png)
试题解析:(Ⅰ)证明:因为四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125336-67195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125336-50721.png)
又因为平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125336-86162.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125336-67195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125339-56725.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125339-14497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125339-19073.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125336-67195.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125337-46365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125337-45870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125339-46580.jpg)
(Ⅱ)证明:在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125340-25842.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125340-17357.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125340-89555.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125337-11891.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125340-99067.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125338-64023.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125340-53025.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125338-64023.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125337-29984.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125338-64023.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125338-23268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125338-61333.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125340-10141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125341-68058.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125341-15926.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125338-58564.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125341-64598.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125338-64023.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125341-67236.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125338-64023.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125338-29618.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125338-64023.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125341-48783.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125342-50760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125342-34432.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125339-91095.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125338-64023.png)
(Ⅲ)解:由(Ⅰ),得
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125342-89505.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125337-45870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125342-87126.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125337-45870.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125342-70302.png)
所以四棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125342-14664.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125343-31772.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125343-72194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125343-34648.png)
所以多面体
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125343-85795.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125343-85462.png)
核心考点
试题【如图,在多面体ABCDEF中,底面ABCD是边长为2的正方形,四边形BDEF是矩形,平面BDEF⊥平面ABCD,BF=3,G和H分别是CE和CF的中点.(Ⅰ)求】;主要考察你对柱锥台的表面积等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125328-23624.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125329-85241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125329-83595.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125329-68753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125329-49934.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125329-85241.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125330-39397.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125330-20419.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125330-87453.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125330-67103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125331-59191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125317-36291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125317-82878.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125317-36291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125312-91661.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125312-43296.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125312-16521.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125312-16671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125313-62629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125313-58913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125313-59253.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125313-48979.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125302-67681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125302-56859.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125302-56244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125303-28681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125303-85466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125302-67681.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125303-86309.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125303-38440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021125304-97257.png)
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