题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135106-53554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135106-71604.jpg)
(Ⅰ)求证:CD⊥平面A1ABB1;
(Ⅱ)求三棱锥A1-CDE的体积.
答案
解析
(2)本小题求面积不易直接求,采用整体减去部分的作法求解.本小题可以用
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135106-95338.png)
(1)在Rt△DBE中,BE=1,DE=
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135106-53554.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135106-38723.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135106-65648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135107-49030.png)
∴ 则D为AB中点, 而AC=BC, ∴CD⊥AB
又∵三棱柱ABC-A1B1C1为直三棱柱, ∴CD⊥AA1
又 AA1∩AB="A" 且 AA1、AB Ì平面A1ABB1
故 CD⊥平面A1ABB1 6分
(2)∵四边形A1ABB1为矩形,∴△A1AD,△DBE,△EB1A1都是直角三角形,
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135107-36948.png)
=2×2
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135106-65648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135107-49030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135106-65648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135107-49030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135106-65648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135107-49030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135106-65648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135107-82740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135106-65648.png)
∴ VA1-CDE =VC-A1DE =
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135107-89129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135107-89129.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135107-82740.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135106-65648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135106-65648.png)
∴ 三棱锥A1-CDE的体积为1
核心考点
试题【直三棱柱ABC-A1B1C1中, AC=BC=AA1=2,∠ACB=90°.E为BB1的中点,D点在AB上且DE=.(Ⅰ)求证:CD⊥平面A1ABB1;(Ⅱ)】;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/20191021/20191021135053-92044.png)
(A)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135053-17018.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135054-34057.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135054-63715.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135054-69742.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135045-63974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135045-11991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135045-78916.png)
求它的体积。
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135040-89160.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135034-94749.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135034-10298.png)
(1)求圆锥的表面积与球面积之比;
(2)求圆锥的体积与球体积之比。
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135019-10762.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135019-23979.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135019-31965.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135020-61397.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135020-71347.jpg)
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