题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121240-22044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121240-86423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121240-94263.png)
(1)求证:AC⊥平面VOD;
(2)求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121240-90245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121241-32497.jpg)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121241-27193.png)
解析
试题分析:(1)证明线面垂直,要证明直线与平面内的两条相交直线垂直,首先
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121241-51433.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121241-63813.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121241-94020.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121242-74433.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121242-61082.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121242-38490.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121242-91092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121243-25228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121243-48697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121243-89114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121243-79480.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121241-63813.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121243-13246.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121244-23555.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121244-86202.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121244-49248.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121244-82054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121244-31759.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121245-91040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121245-91040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121245-21718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121245-73320.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121245-89007.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121245-64145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121241-51433.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121246-99502.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121246-56163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121246-51329.png)
(1)∵VA=VB,O为AB中点,∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121246-21547.png)
连接
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121247-42586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121247-45593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121247-11792.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121247-65084.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121247-45593.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121247-62787.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121248-53226.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121248-28898.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121248-56808.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121247-42586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121248-27660.png)
∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121248-79980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121249-85298.png)
又∵
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121249-18753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121240-22044.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121249-95209.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121249-33995.png)
∵VOÌ平面VOD,VDÌ平面VOD,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121250-97867.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121250-74689.png)
(2)由(2)知
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121245-21718.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121245-91040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121250-37242.png)
又∵点C是弧的中点,∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121246-56163.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121250-21422.png)
∴三角形
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121243-89114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121250-60892.png)
∴棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121245-91040.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121251-76491.png)
故棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121240-90245.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121241-27193.png)
核心考点
试题【如图,AB是圆O的直径,点C是弧AB的中点,点V是圆O所在平面外一点,是AC的中点,已知,.(1)求证:AC⊥平面VOD;(2)求三棱锥的体积.】;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/20191021/20191021121235-55212.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121235-37431.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121235-60514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121236-37024.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121228-24916.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121229-24349.png)
(1)证明: A1BD // 平面CD1B1;
(2)求三棱柱ABD-A1B1D1的体积.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-40678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-52514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-54409.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-31156.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-61672.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-17418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-70103.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-41824.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121217-15123.png)
(3)若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121217-16330.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121217-91708.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121216-40678.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121217-87817.png)
(1)求证:DC∥平面PAB;
(2)求四棱锥P﹣ABCD的体积.
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021121210-50533.png)
A.6π | B.4π | C.2π | D.π |
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