1 . 如图1是唐朝著名的凤鸟花卉纹浮雕很杯,它的盛酒部分可以近似地看作是半球与圆柱的组合体(如图2).当这种酒杯内壁的表面积为
,半球的半径为
时,若要使得酒杯的容积不大于半球体积的2倍,则
的取值范围是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/9/0f7e7567-689d-4069-bb53-3c23df0d3ba2.png?resizew=207)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30ecfda698212594a342565257dc5508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ae196996ab19c015e7f4eb8ba09982e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280b4359132a3119cd6f0413946ccf18.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/9/0f7e7567-689d-4069-bb53-3c23df0d3ba2.png?resizew=207)
A.![]() | B.![]() |
C.![]() | D.![]() |
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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
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3 . 祖暅(公元
世纪,祖冲之之子),是我国齐梁时代的数学家,他提出了一条原理:“幂势既同,则积不容易.”这句话的意思是:两个等高的几何体若在所有等高处的水平截面的面积相等,则这两个几何体的体积相等.如图将底面直径皆为
,高皆为
的椭半球体和已被挖去了圆锥体的圆柱体放置于同一平面
上,用平行于平面
且与
距离为
的平面截两个几何体得到
及
两截面,可以证明
总成立.据此,短轴
长为
,长半轴
为
的椭半球体的体积是( )
![](https://img.xkw.com/dksih/QBM/2022/1/21/2899480687181824/2901571237126144/STEM/5fe2db34-5cef-4538-a57b-9a722d52510e.png?resizew=437)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7f1539bc0f3d6ab6b9e96aa5fd0ba97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18436f0e2391b0ab7537a566fc28204c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ef0cd8fc26307d24ac98ea0556464a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/173d3e1ca62e4825252dddecbefe7b15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/009467e7d7de6caeb1eb01210ccb71ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976260cbf5e30856d4fd37a4b0a671a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c78d0ab561d0c9bb9099772c596af8bf.png)
![](https://img.xkw.com/dksih/QBM/2022/1/21/2899480687181824/2901571237126144/STEM/5fe2db34-5cef-4538-a57b-9a722d52510e.png?resizew=437)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 在等腰直角三角形
中,
,
为
的中点,将它沿
翻折,使点
与点
间的距离为
,此时四面体
的外接球的表面积为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e5e82501f53054b927bf3b668071b75.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-11-14更新
|
584次组卷
|
4卷引用:山西省运城市康杰中学2023届高三上学期期末数学试题