题目
题型:不详难度:来源:
(
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085936-49110.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085936-22600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085936-37393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085936-87856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085936-37393.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085936-71988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085936-23482.png)
答案
解析
分析:根据圆柱体积与球的体积之比是3:2,确定其半径之比,进而可得圆柱的表面积与球的表面积之比.
解答:解:设圆柱底面直径为2R
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085936-95927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085937-23683.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085937-22409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085937-89634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085937-78274.png)
∵圆柱体积与球的体积之比是3:2
∴2πR
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085937-22409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085937-89634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085937-78274.png)
∴R
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085936-95927.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085937-23683.png)
∵圆柱的表面积为2πR
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085937-64535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085937-64535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085937-64535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085937-26441.png)
∴圆柱的表面积与球的表面积之比为6πR
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085937-64535.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085937-26441.png)
故选D.
点评:本题考查圆柱与球的体积与表面积的计算,正确运用公式是关键,属于基础题.
核心考点
试题【一个圆柱底面直径与高相等,其体积与一个球的体积之比是3:2,则这个圆柱的表面积与这个球的表面积之比为( )()1:1 () 1: ()】;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/20191021/20191021085931-20563.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085924-96993.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085924-83755.png)
A.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085925-95362.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085925-95959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085925-93999.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085925-49845.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085918-11128.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085918-43826.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085918-32233.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085919-89423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085919-97630.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085919-27908.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085919-56298.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021085920-49188.jpg)