题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080701-15406.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080701-48228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080702-43791.png)
答案
解析
试题分析:圆柱形圆桶的直径为4R,故第一层可以放入直径为2R的球2个,由于相邻两层四个球的球心正好构成一个棱长为2R的正四面体,故两层球心的连线形成的两条异面直线间距离为:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080702-68141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080702-68141.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080702-22143.png)
点评:此题的关键是确定“层距”。本题易将“层距”误认为为2R。
核心考点
试题【某圆柱的底面直径为高为则它最多能放入半径为的球 个。】;主要考察你对空间几何体的视图与直观图等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080657-16002.png)
(1)画出这个几何体的直观图(不用写作图步骤);
(2)请写出这个几何体的名称,并指出它的高是多少;
(3)求出这个几何体的表面积。
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080657-78751.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080649-71507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080649-79641.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080649-76208.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080650-85592.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080650-44817.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080650-76339.jpg)
(1)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080650-46807.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080651-17799.png)
(2)求
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080651-49472.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080651-55030.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080640-12045.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080640-18949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080640-16294.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080640-10706.jpg)
(I)求证:对任意
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080640-22411.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080640-18533.png)
(II)若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080640-92978.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080641-22365.png)
(III)是否存在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080641-79707.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080641-22234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080641-42760.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080641-88506.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080641-79707.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080625-58525.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080625-76606.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080626-53803.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080626-37974.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080626-36367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080626-94523.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080626-97055.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080627-39124.png)
(2)在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080627-39491.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080627-26268.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080627-35723.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080628-11093.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080628-81020.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080615-88292.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080615-79626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080615-38228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080616-27514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080616-94658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080616-39684.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080616-17567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080616-44809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080616-44809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080616-25327.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080616-61963.png)
(1)设
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080616-43478.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080616-44809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080616-60169.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080616-68496.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080616-60169.png)
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080617-89107.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080616-44809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080617-89099.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080617-37168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080617-37168.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021080617-89099.png)
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