题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131534-97244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131534-77185.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131534-59672.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131534-69799.png)
解析
试题分析:先设梯形的上底、下底和高,然后利用圆柱和圆锥的体积公式求出以这三边旋转得到的几何体的体积,联立得到的式子可解出上底、下底和高,结合勾股定理,另一腰也可求出,故梯形的周长可以得到。
解:设梯形的上底长为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131535-16778.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131535-35558.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131535-33379.png)
则梯形绕上底旋转所得旋转体的体积为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131535-16475.png)
因此
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131536-27551.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131536-53444.png)
同理有
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131536-66023.png)
两式相除得
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131536-17739.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131536-66575.png)
代入
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131536-53444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131537-22452.png)
注意到直角腰长等于高
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131535-33379.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131537-16963.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131536-66575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131537-31389.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131537-22452.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131537-55436.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131538-89652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131538-68779.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131538-87110.png)
点评:找出组合图形的各部分数据,求体积和.
核心考点
试题【一个直角梯形的上底比下底短,该梯形绕它的上底旋转一周所得旋转体的体积为,该梯形绕它的下底旋转一周所得旋转体的体积为,该梯形绕它的直角腰旋转一周所得旋转体的体积为】;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/20191021/20191021131525-34069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131525-90595.png)
A.与x、y都有关 | B.与x有关、与y无关 |
C.与x、y都无关 | D.与x无关、与y有关 |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131526-15093.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131510-60599.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131510-82365.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131510-34002.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131454-27685.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131455-22937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131455-54856.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131455-22937.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131455-47449.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131455-19332.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131456-92843.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131456-80247.png)
(Ⅰ)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131456-20120.png)
(Ⅱ)在
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131456-64444.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131457-98467.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131457-69116.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131457-93122.png)
(Ⅲ)求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131457-74736.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131457-58818.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131444-49188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131444-67179.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131444-49188.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131444-89764.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131444-87588.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131445-96298.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131445-30643.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131445-77015.png)
(Ⅰ)求证:平面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131445-51959.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131446-13050.png)
(Ⅱ)求几何体
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131446-42348.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131433-92167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131433-52797.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131434-37232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131434-18448.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131434-42290.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131434-13846.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131434-54774.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131434-49842.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021131434-25199.png)
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