传说古希腊数学家阿基米德的墓碑上刻着一个圆柱,圆柱内有一个内切球,这个球的直径恰好与圆柱的高相等.由于这个“圆柱容球”是阿基米德生前最引以为豪的发现,于是他留下遗言:他死后,墓碑上要刻上一个“圆柱容球”的几何图形.如图,在底面半径为1的圆柱
内的球O与圆柱
的上、下底面及母线均相切,设A,B分别为圆柱
的上、下底面圆周上一点,且
与
所成的角为
,则
与圆柱
的底面所成角的正切值为__________ ;直线
与球O的球面交于两点M,N,则
的值为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e65ac334119ccd6204402a7aba29a55.png)
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![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/8/55dabb7a-1877-46ad-acf8-28a36094de52.png?resizew=325)
21-22高三上·江西·期末 查看更多[4]
江西省名校2022届高三上学期期末联考数学(理)试题(已下线)数学-2022年高考押题预测卷02(江苏专用)河北定州中学2022-2023学年高一下学期5月月考数学试题(已下线)模块三 专题3 题型突破篇 小题满分挑战练(2)
更新时间:2022-01-24 20:40:11
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【推荐1】在四面体
中,
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【推荐2】四面体ABCD中,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd52c03da84904d1c98e38f91b232520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf157954f8933471199d00e0c74f994c.png)
,二面角A-CD-B的大小为
,则该四面体外接球的体积为________ .
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【推荐1】在等边三角形
中,
为
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【推荐2】在三棱锥
中,已知
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【推荐3】已知△ABC是正三角形,OA⊥平面ABC,且OA=AC=2,则OB与平面OAC所成角的余弦值为_______ ;若点A关于直线OC的对称点为A',则直线AA'与BC所成角的余弦值为______ .
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