题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021071112-60336.png)
(1)若该四棱锥的左视图为直角三角形,则它的体积为__________;
(2)关于该四棱锥的下列结论中:
①四棱锥中至少有两组侧面互相垂直;
②四棱锥的侧面中可能存在三个直角三角形;
③四棱锥中不可能存在四组互相垂直的侧面.
所有正确结论的序号是___________.
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021071112-49942.png)
解析
试题分析:(1)左视图为直角三角形时直角三角形的斜边为2,则斜边上的高为1,此高即为四棱锥的高,所以此四棱锥的体积为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021071112-53180.png)
(2)此棱锥的直观图如图所示,底面
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021071112-62869.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021071112-62646.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021071113-98659.png)
由面面垂直的性质定理可得
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021071113-76565.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021071113-61119.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021071113-34605.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021071114-77402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021071114-35926.png)
核心考点
试题【已知某四棱锥,底面是边长为2的正方形,且俯视图如图所示.(1)若该四棱锥的左视图为直角三角形,则它的体积为__________;(2)关于该四棱锥的下列结论中:】;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/20191021/20191021071109-99658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021071105-15122.jpg)