2022·全国·模拟预测
1 . 已知圆柱
中,AB为底面圆O的直径,
,点P为底面圆O上一点,当圆柱
的表面积为
时,三棱锥
的外接球的体积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7bae5203f4b4acf23779114b3466e17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192f4f9446c954a291f779d963f90257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6bd8db8362626db8d6a8d8ebdbd1562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/793c8b11497434597989b646768d2039.png)
您最近一年使用:0次
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解题方法
2 . 如图正方体
的棱长为4,点M是棱
的中点,点P在面
内(包含边界),且
,则下列四个命题中:
![](https://img.xkw.com/dksih/QBM/2022/1/27/2903564803244032/2938839180140544/STEM/1449dfd91d1848379d24787a95b2701f.png?resizew=156)
①点
的轨迹的长度为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9fdc1f8ed0ae44b54a9a2a3aca2db4.png)
②存在
,使得![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a53ed1ecd56f1d951001c111cb1563.png)
③直线
与平面
所成角的正弦值最大为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
④沿线段
的轨迹将正方体
切割成两部分,挖去体积较小部分,剩余部分几何体的表面积为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74be65f77a725cbed17ba0a310033352.png)
其中正确命题的序号是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce932cc5e92720f4ae35492c2f1a068.png)
![](https://img.xkw.com/dksih/QBM/2022/1/27/2903564803244032/2938839180140544/STEM/1449dfd91d1848379d24787a95b2701f.png?resizew=156)
①点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e9fdc1f8ed0ae44b54a9a2a3aca2db4.png)
②存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a53ed1ecd56f1d951001c111cb1563.png)
③直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bf9ef324f1289e205e29fed105c38e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
④沿线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74be65f77a725cbed17ba0a310033352.png)
其中正确命题的序号是
您最近一年使用:0次