题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080642-58586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080642-23150.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080642-68717.png)
A.2![]() | B.3![]() | C.![]() | D.6 |
答案
解析
分析:设出正方体的三度,利用面积公式求出三度,然后求出对角线的长.
解:设长方体三度为x,y,z,
则yz=
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080642-58586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080642-23150.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080642-68717.png)
三式相乘得x2y2z2=6,xyz=
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080642-68717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080642-23150.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080642-58586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080643-19208.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080643-80874.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080642-68717.png)
故选D.
核心考点
举一反三
如图,已知四棱锥P—ABCD的底面是直角梯形,∠ABC=∠BCD=90o,AB=BC=PB=PC=2CD=2,侧面PBC⊥底面ABCD,O是BC的中点,AO交BD于E.
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080633-53103.gif)
(1)求证:PA⊥BD;
(2)求二面角P—DC—B的大小.
如题18图,平行六面体
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080624-33398.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080625-59554.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080625-27499.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080625-31656.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080625-24126.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080625-59554.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080626-24442.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080626-20726.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080626-10760.gif)
(Ⅰ)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080626-19137.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080627-43208.gif)
(Ⅱ)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080627-36726.gif)
如图,在四棱锥V-ABCD中底面ABCD是正方形,侧面VAD是正三角形,平面VAD
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080614-28126.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080615-37072.jpg)
(1)证
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080615-94429.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080615-84609.gif)
(2)求面VAD与面VDB所成的二面角的余弦值。
如图在三棱锥P-ABC中,PA
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080601-54389.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080602-78900.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080602-96545.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080602-61414.jpg)
(1)求证:BC
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080602-93980.gif)
(2)当D为PB中点时,求AD与平面PAC所成的角的余弦值;
(3)是否存在点E,使得二面角A-DE-P为直二面角,并说明理由。
如图a,在直角梯形
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080552-47815.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080552-66504.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080552-37549.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080553-12629.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080553-35694.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080553-26235.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080553-65884.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080554-35409.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080554-16709.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080554-17422.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080554-85665.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080554-85665.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080554-15126.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080555-68999.gif)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080555-59772.gif)
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080555-77642.gif)
(2)求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191022/20191022080555-47955.gif)
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