题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134702-50115.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134702-83065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134702-91466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134702-66317.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134702-91466.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134702-83065.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134703-16438.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134703-19235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134703-85860.png)
(1)求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134703-44422.png)
(2)求异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134703-46339.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134704-48536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134704-33407.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134704-62096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134704-50084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134705-31301.png)
解析
(1)因为根据已知条件中圆柱的表面积和长度和角度问题可知得到锥体的底面的面积的求解以及最终的体积的表示。
(2)因为异面直线的所成的角一般通过平移得到,那么平移后的夹角为所求的异面直线的角。
解:
(1)由题意
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134705-79215.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134705-90238.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134705-97353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134706-33454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134706-63199.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134706-41946.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134706-16897.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134707-50021.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134704-62096.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134704-50084.png)
(2)取
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134707-87924.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134707-40937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134707-32826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134707-20746.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134708-98464.png)
得
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134708-68743.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134703-46339.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134708-81702.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134708-91717.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134709-10515.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134709-31817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134709-74783.png)
由余弦定理得
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134709-91981.png)
所以异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134703-46339.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134704-48536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134705-31301.png)
核心考点
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134655-41097.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134655-34607.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134642-18685.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134642-83248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134642-53929.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134642-50956.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134642-82257.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134643-96676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134643-44121.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134643-76952.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134642-83248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134644-64774.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134644-38912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134644-32089.png)
(Ⅱ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134644-90592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134644-16033.png)
(Ⅲ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134645-11900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134645-28231.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134645-27373.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134628-31968.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134628-11229.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134605-54872.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134605-62381.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134605-50887.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134605-62381.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134605-35392.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134606-10222.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134606-11534.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134606-10146.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134607-83570.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134607-67460.png)
(2)若四面体
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134607-64648.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134607-20430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021134608-10458.png)
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