题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000337-33978.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000338-71935.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000338-18239.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000338-18239.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000338-37669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000338-10924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000339-21976.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000340-50913.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000340-34824.png)
(I)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000340-57215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000340-47994.png)
(II)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000340-32082.png)
(III)设PD="AD=a," 求三棱锥B-EFC的体积.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000341-44342.jpg)
答案
(Ⅱ)证明见解析
(Ⅲ)∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000341-28082.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000341-41249.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000341-99224.png)
第二问中,利用
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000342-16817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000342-89136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000342-84195.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000342-21493.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000343-97561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000343-28411.png)
第三问中,借助于等体积法来求解三棱锥B-EFC的体积.
(Ⅰ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000343-50572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000343-73472.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000344-88023.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000341-41249.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000344-21157.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000341-99224.png)
(Ⅱ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000343-50572.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000338-18239.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000342-16817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000344-22680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000342-89136.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000342-84195.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000344-70712.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000342-21493.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000343-97561.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000343-28411.png)
(Ⅲ)解:连接AC,DB相交于O,连接OF, 则OF⊥面ABCD,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000344-54153.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000345-21993.png)
核心考点
试题【如图,在四棱锥中,⊥底面,底面为正方形,,,分别是,的中点.(I)求证:平面;(II)求证:;(III)设PD="AD=a," 求三棱锥B-EFC的体积.】;主要考察你对空间几何体的结构特征等知识点的理解。[详细]
举一反三
A.4个 | B.2个 | C.3个 | D.1个 |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000327-82901.png)
A.12π | B.18π | C.36π | D.6π |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000314-25427.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000314-70911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000314-70911.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000315-35483.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000315-35483.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000315-46111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000315-46111.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000300-83419.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021000300-15967.png)
(1)证明在侧棱AA1上存在一点E,使得OE⊥平面BB1C1C,并求出AE的长;
(2)求平面A1B1C与平面BB1C1C夹角的余弦值。
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