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1 . 把圆心角为90°的扇形铁片围成一个侧面积为16πm2的圆锥(接缝处忽略不计),该圆锥竖直倒置后放入一个球,该球恰好与圆锥的侧面上边缘相切,则球心到圆锥顶点的距离为__________ m.
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2020-12-24更新
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172次组卷
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3卷引用:河南省鹤壁高中2021-2022学年高三上学期一轮复习质量检测(二)数学(文)试题
2 . 如图是某品牌手机的商标图案,制作时以曲线段
为分界线,裁去一部分图形而成,已知该分界线是一段半径为
的圆弧,若圆弧的长度为
,则
两点间的距离为( )
![](https://img.xkw.com/dksih/QBM/2021/1/5/2629446249357312/2629768923217920/STEM/94091ece4bda45de98d6b2cb633d5263.png?resizew=48)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b709fca5e6d818c1ef72b50da972dfdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://img.xkw.com/dksih/QBM/2021/1/5/2629446249357312/2629768923217920/STEM/94091ece4bda45de98d6b2cb633d5263.png?resizew=48)
A.![]() | B.![]() | C.![]() | D.![]() |
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2021-01-05更新
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126次组卷
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2卷引用:江苏省扬州市2020-2021学年高三上学期1月适应性练习数学试题
3 . 希波克拉底发现了平面几何里应用广泛的月牙定理,即以直角三角形两条直角边为直径向外作两个半圆,以斜边为直径向内作半圆,则三个半圆所围成的两个月牙型面积之和等于该直角三角形的面积.如图所示,阴影部分的月牙形的边缘都是圆弧,两段圆弧分别是
的外接圆和以
为直径的圆的一部分,若
,
,则该月牙形的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d3a7e3355ee508b11f19c15e28dfeab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ad3a578f403b9e6b97fa2dc955fc11.png)
![](https://img.xkw.com/dksih/QBM/2021/3/17/2679721564389376/2684893970276352/STEM/16c323010b60484280b71e1c35d5115f.png?resizew=101)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 如图所示,某传动装置由两个陀螺
,
组成,陀螺之间没有滑动,每个陀螺都由具有公共轴的圆锥和圆柱两个部分构成,每个圆柱的底面半径和高都是相应圆锥底面半径的
,且
,
的轴相互垂直,它们相接触的直线与
的轴所成角
,若陀螺
中圆锥的底面半径为
(
);
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/44a822b3-0a30-4f6b-bccd-69ac6b2c1d62.png?resizew=216)
(1)求陀螺
的体积;
(2)当陀螺
转动一圈时,陀螺
中圆锥底面圆周上一点
转动到点
,求
与
之间的距离;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6812ad2f71f945d641ed56c4bddc5a60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba6b6aa6c3f9faba6b03bc193a6e61.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/44a822b3-0a30-4f6b-bccd-69ac6b2c1d62.png?resizew=216)
(1)求陀螺
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
(2)当陀螺
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9275bd8ce17fcc4a786510b008414ab0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9a724b59c890095baa5cb73e267c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
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2020-01-14更新
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144次组卷
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2卷引用:上海市格致中学2022届高三上学期十月月考数学试题
2011·上海静安·一模
5 . 如图,用半径为
cm,面积为
cm2的扇形铁皮制作一个无盖的圆锥形容器(衔接部分忽略不计),该容器最多盛水多少?(结果精确到0.1cm3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fa0199c2165defca15cdf44249b0fd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74dafe5bdaa25ec46bac928980ea125e.png)
![](https://img.xkw.com/dksih/QBM/2011/5/6/1570182210019328/1570182214975488/STEM/8b4fdb91dd6c4312bd8f8878858fefaf.png?resizew=225)
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