名校
1 . 如图,四边形
是圆柱的轴截面,
是母线,点D在线段BC上,直线
//平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/6/3c7749db-d433-4ec9-baa9-110956159ab3.png?resizew=161)
(1)记三棱锥
的体积为
,三棱锥
的体积为
,证明:
;
(2)若
,
,直线
到平面
的距离为
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b7b7793d29d66dfdd89e7a6564a35c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5888bec948373f3854258ad80171073d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/6/3c7749db-d433-4ec9-baa9-110956159ab3.png?resizew=161)
(1)记三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e98058f394b0d5b4d8498b2dcfa3983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42e4d3ce220fd60e952c957fb71a6d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e449727158281e3370255436481a848.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267880e605306851d8f46be77b11f9c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4b6c682d7b0741fb1f12a073394fc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5888bec948373f3854258ad80171073d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d599cb4a589f90b0205f24c2e1fa021e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5888bec948373f3854258ad80171073d.png)
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2023-05-05更新
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2卷引用:福建省福州市2023届高三质量检测数学试题