已知
是球
的球面上的四点,
为球
的直径,球
的表面积为
,且
,
,则直线
与平面
所成角的正弦值是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95345846d2dd4dfa042a9093c62a8b82.png)
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2022·湖南常德·一模 查看更多[6]
湖南省常德市2022届高三下学期一模数学试题福建省厦门双十中学2022届高三下学期高考热身考试数学试题(已下线)专题07 立体几何初步宁夏银川一中、云南省昆明市第一中学2023届高三联合考试一模数学(理)试题(已下线)宁夏银川一中、云南省昆明市第一中学2023届高三联合考试一模数学(理)试题(已下线)专题12空间向量与立体几何(选填题)
更新时间:2022-03-29 09:26:29
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【推荐1】已知三棱锥
中,
,且
,长度为1的线段
的端点
在
上,端点
在侧面
内运动,若
的中点为
,
的重心为
,则
的最小值是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81ff2c282e317373b88cb632ad96b195.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
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【推荐2】已知球
的半径是1,
三点都在球面上,
两点和
两点的球面距离都是
,
两点的球面距离是
,则二面角
的大小为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
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【推荐1】已知某几何体的三视图如图所示,则它的外接球表面积为________ .
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/18/b57e8790-5d6f-4985-859c-94a3907d7574.png?resizew=210)
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【推荐2】将一个圆心角为
、面积为
的扇形卷成一个圆锥,则此圆锥内半径最大的球的表面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0211da37e92f915e781691296578ba0.png)
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【推荐1】已知
平面
,四边形
是平行四边形,若
,则平行四边形
一定是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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【推荐2】在棱长为1的正方体
中,点
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平面
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的长的取值范围是______ .
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f369bec2d5682bf6b8b317a08aff546.png)
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【推荐3】在三棱锥
中,
两两垂直,
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为棱
上一点,
于点
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【推荐1】设二面角
的大小为45°,A为棱上一点,
在
内与
成45°角,则
与平面
所成角的大小为_____ .
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【推荐2】如图,在正方体
中,点
为线段
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在线段
上,直线
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【推荐3】三棱锥
中,点
是
斜边
上一点.给出下列四个命题:
①若
平面
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的四个面都是直角三角形;
②若
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,
,
平面
,则三棱锥
的外接球体积为
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③若
,
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,
在平面
上的射影是
内心,则三棱锥
的体积为2;
④若
,
,
,
平面
,则直线
与平面
所成的最大角为
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其中正确命题的序号是__________ .(把你认为正确命题的序号都填上)
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①若
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②若
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③若
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
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④若
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65a3e478bb87d094e3a0af30dd10ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f643db1101c352132c1d670e9cb30e.png)
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其中正确命题的序号是
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