题目
题型:不详难度:来源:
![](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)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135020-64835.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135020-27079.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135021-33567.png)
解析
(1)因为多面体ABCDS的体积即四棱锥S—ABCD的体积。利用棱锥的体积公式求解得到。
(2)分析; 要求AD与SB所成的角,即求BC与SB所成的角,那么利用平移法得到角,解三角形得到结论。
(3)利用三垂线定理得到二面角,然后借助于三角形的知识求解得到。
解:(I)多面体ABCDS的体积即四棱锥S—ABCD的体积。
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135020-64835.png)
II)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135021-53985.png)
|
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135021-57937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135021-57937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135021-44651.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135022-57991.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135022-17824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135021-57937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135022-36452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135022-29354.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135022-22431.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135021-57937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135023-54358.png)
从而SB与AD的成的角的余弦为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135020-27079.png)
(III)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135023-25567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135023-64060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135023-11225.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135024-25107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135024-47523.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135024-39409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135024-64494.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135025-56140.png)
在矩形ABCD中,对角线
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135025-61075.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135025-36359.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135025-34806.png)
由(2)知在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135026-13993.png)
而
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135026-12701.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135026-76102.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135026-14756.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135026-26680.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135027-98068.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135027-66153.png)
所以所求的二面角的余弦为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135021-33567.png)
核心考点
试题【如图,多面体ABCDS中,面ABCD为矩形,且, 。(I)求多面体ABCDS的体积;(II)求AD与SB所成角的余弦值;(III)求二面角A—SB—D的余弦值。】;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/20191021/20191021135013-97440.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135013-41297.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135013-71417.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135014-19887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135014-49563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135014-97589.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135014-97589.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135014-19887.png)
①的式子: ……②,
②式可用语言表述为: .
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135008-91487.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135008-20122.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135002-80371.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135003-98697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135003-76574.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021135004-34212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134951-94242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134951-45374.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134951-70046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134951-94242.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134951-80270.png)
A.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134952-96315.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134952-35670.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134952-88383.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134952-81008.png)
A.6 | B.36 | C.![]() | D.2![]() |
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