如图所示,已知等腰梯形ABCD的上底AD=2 cm,下底BC=10 cm,底角∠ABC=60°,现绕腰AB旋转一周,则所得的旋转体的体积是( )
![](https://img.xkw.com/dksih/QBM/2021/4/16/2701121854660608/2701675343224832/STEM/4bf5a0b34d6647cd8efe0022e8f92c32.png?resizew=171)
![](https://img.xkw.com/dksih/QBM/2021/4/16/2701121854660608/2701675343224832/STEM/4bf5a0b34d6647cd8efe0022e8f92c32.png?resizew=171)
A.246π | B.248π |
C.249π | D.250π |
2021高三·全国·专题练习 查看更多[1]
(已下线)专题08 立体几何-备战2021年高考数学(理)纠错笔记
更新时间:2021-04-19 15:34:42
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【推荐1】将半径为3圆心角为
的扇形围成一个圆锥,则该圆锥的内切球的体积为( )
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【推荐2】在等腰三角形
中,
,顶角为
,以底边
所在直线为轴旋转围成的封闭几何体内装有一球,则球的最大体积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
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【推荐1】如图,平面四边形
中,
,
,
,
,
,则四边形
绕
所在的直线旋转一周所成几何体的表面积为( )
![](https://img.xkw.com/dksih/QBM/2023/7/5/3274316053561344/3288793654812672/STEM/3cd946ac1290400bba92173757e4a10f.png?resizew=108)
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【推荐2】祖暅(公元5-6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,则积不容异.”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.该原理在西方直到十七世纪才由意大利数学家卡瓦列利发现,比祖暅晚一千一百多年.椭球体是椭圆绕其轴旋转所成的旋转体.如图将底面直径皆为
,高皆为a的椭半球体及已被挖去了圆锥体的圆柱体放置于同一平面
上.以平行于平面
的平面于距平面
任意高d处可横截得到
及
两截面,可以证明
总成立.据此,短轴长为
,长轴为
的椭球体的体积是( )![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc6d1d99afa158b4ba4fc0dae562fcc1.png)
![](https://img.xkw.com/dksih/QBM/2021/5/7/2715794356944896/2760759051927552/STEM/d316fce6-3115-4ea0-8864-85eb4628b70d.png?resizew=350)
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