解题方法
1 . 由曲线
围成的封闭图形绕
轴旋转一周所得的旋转体的体积为
;满足
的点
所组成的封闭图形绕
轴旋转一周所得的旋转体的体积为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/9/ff4c3def-8c4e-4174-9496-7c9e1a7b36c3.png?resizew=426)
(1)当
时,分别求出两旋转体的水平截面的面积
;
(2)求
与
的关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a16473364f2beecf1e4404987cd7e1c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31ad9babbb0800e2fac1895399e24e01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0203b006524305c3d8ee0b6c34cd872b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/9/ff4c3def-8c4e-4174-9496-7c9e1a7b36c3.png?resizew=426)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbaa8af08dcb2eb604779d01a4cab47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3637753af5ce86be9c23a9beb6b5067.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
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2 . 已知棱长为2cm的正方体容器内盛满水,把半径为1cm的钢球放入水中,刚好被淹没;然后放入一个铁球,使它也淹没于水中.要使流出的水量最多,这个铁球的半径应为多少?
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